The beauty of 4th gen is that the games are accessible (as in easy to learn controls and intuitive gameplay), easy to make time for (you can beat a lot of games in an hour or less unless it's an RPG or a Zelda game), and the graphics for a lot of games (particularly the SNES) still hold up. Put simply, 4th gen is both timeless and easy to work into any busy gamer's life.
It's so easy to pick up a handheld like a Retroid Pocket 5 or modded Vita with some emulators, blow through a game of Star Fox or Streets of Rage 2 or whatever in like 30 minutes, and then get back to your busy life. That's what I love about the 16-bit era. I don't ever see a time in my life where I'll be too busy to play those games, unlike many modern games.
Plus, the overall difficulty of a lot of games wasn't as high as the notorious 8-bit era so you didn't have to stress as much. You've got much better odds of beating Battletoads in Battlemaniacs then you do Battletoads on the NES. Mega Man X was way easier than Mega Man, and Super Castlevania IV wasn't as brutal as earlier 8-bit installments. 4th gen was like the 3rd gen refined. Things played better, looked better, and sounded better.