This actually started a couple weeks ago as a much narrower-in-scope post, focused almost exclusively on things that I don't like about tactical RPGs. That soon grew into RPGs in general, and then into games in general, so why not just cover everything at once?
Player agency
I'm a big fan of arcade-style games, where the purpose is largely to get a super-high score, beat the game in one sitting, or at the very least, survive as long as you can. It's no surprise, then, that player agency, when pulled off well, is a big selling-point for me. This is easy to attain in games of skill - you, as the player, have a direct impact on how well you will do. If you can't react quick enough, if you don't have the right timing, if you're not familiar with the game's mechanics, you will suffer greatly for it.
On the opposite end (where I consider most traditional, strategy, and various other subsets of RPGs to be), are very player-distant games. You do not act directly (usually), but dictate commands to your avatars, who then carry out those actions on their own. Now, obviously, there's a bit of a stretch to be made, here. You, as the player, are an agent using your strategy (not necessarily a raw skill) to affect the game and the characters - you choose the commands, that's your interaction. Not every game can be nonstop blood-pumping alien-shooting action, nor am I suggesting that's what we need.
Turn-based games are particularly difficult to stomach for this. You select a command, it gets carried out, you see the result, then you do it again next turn. The separation between player and action isn't the only thing that bothers me about this - sometimes (or most times), the context just doesn't make sense.
Example: take any of the Fire Emblem games. You direct individual units to move, attack, support, use items, etc. And after a unit is done...it stands there, waiting to be attacked, until the next turn. Clearly, there's a lot of concessions for believability to be made in any game, and I'm not one to tote 'realism' as a compelling aspect for everything, but...really? In what context does it make sense that, before or after someone takes an action, they stand / sit / float with their thumbs well up their asses? Reminds me a lot of military tactics from long-bygone eras, where the strategy of choice was to line up neatly, march forward, and get killed. Or pull up alongside another ship, blast (and get blasted by) it to hell, hope that you're just a little bit better-equipped...and...well, you get the idea.
Where turn-based actually works is when the scale of the game supports it. I'll use a non-RPG, but still turn-based tactics, to exemplify this: Advance Wars. The scale is no longer individual people, but larger forces - a squad of soldiers, group of tanks, flight of jets, etc. So the believability here is better: it takes time to move these units; when they attack, they can't really pull away instantly, and information is naturally less precise (more on this later). Likewise, the 'map' on which your units move reflects this. In my opinion, as the scale increases, the effectiveness of a turn-based situation increases.
I just can't cotton to the process of stand, walk-attack-stand-get attacked that is either poorly implemented, entirely out of context, and / or not explained in the least.
Timing in taking an action
For turn-based games especially, this is almost universal - you have as much time as you damned-well please to plan your move, trial your move, cancel that move, try something else, cancel, then go back again (ad nauseum). This leads to a lot of second-guessing, and drawing out a single turn (and by extension, an entire game) way longer than it needs to be. This gets on my nerves even more when there's a lot of info to be gleaned just by making all these false moves.
There is a counter-point / partial remedy to this: situations where there is fog-of-war. However, it's not used nearly enough; see my points on intel down below for more expansion.
Perfect information and determinism
As games grow in complexity, there's naturally going to be a lot more information to track. The bad part of this is, there's that much more that can be imparted to the player, but I would argue that we should be telling them less, not more. Couple information overload with the movement issues above, and you've got a game that is more or less a purely deterministic affair. You, as the player, receive so much information, so easily available, with so little consequence, that you can scrape every bit of it before making you first move (hell, that's ostensibly what strategy guides are for).
What's more, some games are laid out in such a way that any given action will always do the same thing every time, and you'll know, perfectly, what the results will be. Oh, iron sword plus five attack at one hundred percent hit against three armor will do seven damage. Every time; yes, even that time you fake-moved to see what the result would be ten turns ago. RPGs are terrible, terrible games for this - everything is a number, and the player can see that number, and they know how to make that number go up.
Now, clearly, this is pretty easy to solve with a bit of randomness, but there's another way - don't show all that information to the player! Or, hell, don't allow trial moves! Give some gravity to every move the player makes. Don't allow them to go back - commit them to their first choice. Put more thinking up front! That's not to say that randomness is a panacea, no. Almost every game already does this, but it's applied to such deterministic things that it really doesn't make much of a difference.
Which leads us right to...
Min-maxing; grinding; or, strategies for the uninspired
Min-maxing. If a game can be boiled down to this, you may as well not even bother playing more than once, if at all. It's true, every game is a mathematical construct of some sort, but when the structure, mechanics, and implementation enforce this to such a high degree, it can scarcely be called more than an exchange of time (or money, a topic for another time) for a pretty screen of high numbers.
On a related note, any game that allows infinite progression of these numbers, in any part of the game, there's a pretty big design flaw there. Players are deathly afraid to be challenged, and any opportunity they can get to grind their numbers higher before they really need them is...well, pathetic.
One fairly universal solution is to disallow absolute positive progression. Sure, you can have stuff progress as the game wears on (duh), but level them off and apply different negative effects, too. There's so many strategic elements that could be invoked here, but by and large the go-to thing is to 'see number, make go up'. One method I'd like to see employed more often to discourage grinding is scaling difficulty with the player.
Which brings us to...
Discrete levels
Discrete levels. I'll concede that this is more a legacy thing, something born of a technological limitation to reduce the complexity in play for a given action (and, I'll also concede, there are good and bad implementations of it). But like turn-based actions on the scale of individual characters, it's almost always used in a context that is almost impossible to believe.
Let's say I get in a fight. After said fight, I will be more experienced in fighting (makes sense). Then another one, but after (or even during) I am suddenly so much better - stronger, faster, whatever. What the hell? Sounds absolutely ridiculous, right? There's a discrete level at work. Look, I'm all for indicating to a player that their characters are getting better, but making an(other) number go up at some arbitrary time isn't the way to do it. If anything, you could consider getting ever-so-slightly better with each action taken. Don't jump them up suddenly, just scale the effects continuously.
Now, this may be an issue more with living, breathing characters. For something like - I don't know, a tank - upgrading armor or weapons or engine or whatever can very well be discrete without being ridiculous about it.
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Now, I've done a fair amount of complaining and griping, but here's where it applies - our current game project is a tactical RPG, one very much in the vein of Fire Emblem, and others of the sort which match, almost to a T, the things I've mentioned above. So that puts us in a position to break out of these bad spots, experiment a little, and develop a much more fun, dynamic, and rewarding experience.