The true reason is because it's a requirement that the console manufacturers enforce if you want to create games for their systems. PC games don't have requirements like this.
There are some convenient side effects of the Press Start screen, though, which probably help explain why the requirements exist:
- When a user presses start, the game knows who's "in control" of the game at the moment. This means the game can do nice things like display the game environment in appropriate context. For example, if you have a saved character, the game can show that character.
- It's a convenient place to put branding info, like company logos and such, as well as whatever legal text might be necessary or stuff like ESRB info.
- It's a good landing page for the (also required) "Attract Mode" that shows something interesting every so often like a movie or some gameplay.
- The game can load up the Press Start screen while other stuff is loading in the background. It gives the player something to look at if the intro movies are over but the rest of the game's front end isn't ready to go. You might notice that some Press Start screens actually don't show the "Press Start" text until several seconds after the screen appears (and if you noticed that, you're pretty dang observant, good job!).
If we didn't need a Press Start screen, I think we'd just skip making it most of the time (unless we wanted some of the benefits above I guess).
Note also that downloadable games may have different requirements than full retail games, so this might not be consistent across all the console games you've played lately.