A case of Fridge Logic. Reading the trivia section of Assault Horizon, there would have been sequences involving vertical takeoff with the F-35B if not for technical limitations. Lethal Skies, Airforce Delta Strike and Aero Elite/Aero Dancing 4, three of many a rival to Ace Combat, featured missions that required the use of V/TOL aircraft for their missions, as well as using the vertical take off features of said aircraft. The fridge logic? THE AFOREMENTIONED THREE GAMES WERE ON THE PLAYSTATION 2!!!
There are always limitations on what you can do. For example, early on we wanted to have a V/STOL version of the F-35 - the F-35C [yes we all know it's the F-35B] – involved in the game. I wrote a really cool mission for it, which would have shown off all of the real airframe’s capabilities. But that proved just too ambitious – maybe in Ace Combat 8.
Also, "technical limitations" isn't just limited to the hardware. The game's engine may not have been built to support V/STOL aircraft. In fact, if memory serves, none of the Ace Combat games have ever supported the V/STOL functionality of aircraft capable of it. (Though this Troper doesn't understand why Assault Horizon doesn't, exactly - the game very explicitly supports both fixed-wing and rotary-wing aircraft; it should not have been too hard to treat the F-35 as the former in flight and the latter during V/STOL segments. Probably on-the-fly switching would've been more difficult to implement, though - the control schemes for aircraft and for rotorcraft are very different.)
Another possibility is that there just isn't much to show off about the airframe. Aside from being able to take off from small places, the F-35 acts just like a regular strike fighter. The main reason it's used is because rapid deployment forces like the U.S. Marines don't like having to lug a big ship like an aircraft carrier around when they go places.
Watching a news program on the F-35 this week suggests that certain details about the fighter, specifically the V\STOL, are classified. When it appeared in earlier games it was built up to be one of the better aircraft however Real Life technical problems had since revealed it not to be the superfighter it once was, so how the V\STOL worked on the plane might not have been left to guesswork.