I unfortunately don't have a lot of technical knowledge to contribute (and frustratingly, there's a lot of "No it isn't", "Yes it is" going on in this thread; wish folks would add a few case studies like Beril did of Gunman Clive to help prove or disprove usefulness in implementation.) This is a question I echo of the OP. so even if the answer is that modern games can't do it, less "you're dumb" and more "here's why it can't work" would be much appreciated.
Street Fighter, especially, I cannot believe they have not learned how to minimize loading downtime in all these years. (In fact, Capcom has actually forgotten things, like where is the Quick Load feature as seen in Street Fighter Alpha 3?) Loading into and out of the character/stage select sequences is abysmal, I have to believe that a version of the Select menu could be resident in memory, even if it was notably pared down from the current one. A world map background, 2D versions of the 12 or so character portraits (and their thumbnails,) the stage graphics, a few overlay PNGs for effects if you can't get that done with vector art or 3D overlays... I just can't imagine Street Fighter being so tight on RAM (especially since other games have multiple characters and/or interactive backgrounds, though the complexity/dissimilarity of characters in SF might negate that argument) that it couldn't keep those things in and out of fights. I can abide by the time it takes to load characters and stages, but the load out of a match into the menus is a huge dampener that negates all the flashy presentation and can kill the buzz of a good party.