I've had Phoenix Wright on the mind on and off. I was really sick yesterday, and built a Phoenix Wright engine. It's certainly not something perfect, but it made me think that maybe I should explain some of the details about what makes Phoenix Wright games Wrightlike.
It's easy to say "the writing", but that's a copout. Let's go over some of the facets that give these games their particular feel.
The most important aspect is that these games are relentlessly linear. There is one specific route forward, no deviations, no branches, no nothing. While there is space to explore, it's 90% color. Because the game is so linear, all the writing effort can be spent on the scenes that will definitely happen, knowing full well the exact path the player took to get here.
This is quite a limitation, but like all limitations, accepting it can open up new vistas of possibility. In this case, the super-rich environments and characters are possible only because of this limitation, and the way each case ticks over into the next with a strong continuity is also because of this.
Nearly all the writing and gameplay elements stem from this relentless linearity.
For example, the pacing of a Phoenix Wright game is a simple but unusual factor. I think of any part of the game as having a pacing which is the risk divided by the exploration capability.
In "exploration" mode, the only real risk is that the player will quit. And there's lots of places to explore. So it's a low-paced part of the game.
In "court" mode, there is some well-defined risk of losing health if you do specific things, but there's also a fair amount of riskless exploration in pushing and listening. So this is a kind of medium-paced part of the game.
In "lockbreak" mode, every move you make is a health risk. There is absolutely nothing to explore. This laser-like focus makes this the most pushingly-paced part of the game.
In actuality, I split these three up into five, because exploration mode has three grades: "wander" mode in early midgame where you get to explore loads of places, "investigate" mode where the number of places is reduced and the amount of interplay between objects increases, and "inspect" mode, where there are only a few places you can go/people you can talk to (for example, if you're locked in a basement).
These pacing tricks can be extrapolated out into a wider variety of games - the amount of risky exploration/choice vs the amount of risk-free exploration. Through this lens, you can see a lot of games taking the same kind of approach. However, there are also games where you have risk-free zones that have no real exploration - hubs, basically. These hubs are very useful to a not-so-relentlessly-linear game where you might have the option to customize things or take different approaches.
Another factor to the Wrightlike games is their puzzles. The puzzle quality varies - it isn't rare to fall out of synch with the script writers and end up either stuck or trying desperately to solve a puzzle that isn't what they want you to solve.
However, setting aside the quality, the puzzles have a slightly unusual timbre to them. The puzzles are relentlessly linear, as mentioned. Unlike normal adventure game puzzles, there's not a world where several puzzles lie in wait. The puzzle coming down the line in a Wrightlike game is the only puzzle, at least at the moment. Other puzzles may be tied to it, but they cannot be dealt with at the present time.
This means that all the inventory stuff, color text, and hints you give out are focused like a laser on the next puzzle. This is a distinctively different feel than you get from an adventure game where there might be four puzzles itching at the back of your mind while you collect stuff.
I think this gives the Wrightlike games an unusually tight, fluid flow to them. Of course, it also gives them a clogged-drain-style flow when the player can't solve a puzzle, which is a downside. Being forced to replay a mission after losing too much health is also unusually onerous, since you have to go through things in precisely the same order again.
Anyway, I'm not normally a fan of linear games. However, to paraphrase Ebert, I may disapprove of a game for going too linear, and yet have a sneaky regard for a game that goes much, much more linear than merely too linear. Embracing this linearity is, I think, what makes Wrightlike games so unique and enjoyable.