The problem is not so much the prompt, but the frequency of it - after every single segment switch. PC version also doesn't autosave, but the prompt is presented only at the completion of a full level.
The nice thing about the PS2 method - it allows you to have a saving point for every segment in the game, which means you can replay individual sections any time you want, and even with all the original lums and bosses still there.
Even that has problems though - to have a save for every point in the game you need a large memory card (32MB), browsing such large cards really slows down the game when transitioning between levels, and navigating the saves is difficult, because they give no useful information as to the exact location when the save was taken.
All in all - more trouble than it's worth.