I do occasionally when I feel like it because I enjoy reliving the good ol' days.
Right now I am making it one of my current projects to revisit just about every old Pokemon game that I own pre-Gen 8 and building teams with them, and in doing so I also currently take interest in studying the game design and structure of each Pokemon game that has existed thus far, down to the level curve, what the game wants me to do and where to go, and whatnot, and it's incredibly interesting to me to see to study what each game was trying to do and how Pokemon game design philosophy has changed over the years and across the games, and in some ways by revisiting many of them in hindsight I have newfound appreciation for many older Pokemon games and like them more when playing them in retrospect than I did when I played them when they were new.
A big thing I am trying now is to use rotating teams of more than six in many of these games, even in games where the EXP All wasn't a thing. Sometimes it's a semi-rotational team where my early team composition is built of early game crutches such as the early bugs and the mammal, which I eventually ditch and replace with later game mons who evolve later as the game goes on, and rinse and repeat. Sometimes it takes grinding, which I feel is particularly a pain in RBY, but fortunately Gens 3, 4, and 5 are very generous with making grinding both easier and more fun thanks to either Trainer rematches in Hoenn and Sinnoh or great training spots in Unova, which is a wonderful treat. It's interesting to look at these games with the intention of studying them and how they were designed, which allowed me to look at them through a different perspective and see how the design philosophy of Pokemon games has changed over the years.
Also with these new playthroughs I have also made efforts to use mons I had never used previously. But most of all is actually trying to integrate the region's pseudo-legendary into my team each and every time. As much as I adore the pseudo-legendary group, until recently I never actually used the pseudo-legendary on my in-game team because I never had the guts or the patience to train one, but now I am repeatedly making it a personal goal to try to get the generation's pseudo-legendary in each game and reap the benefits of it in the end-game. I do not use "old-gen" pseudos in said games though: so in other words, I stick specifically to Garchomp in Diamond and Platinum, Hydreigon in BW and BW2, Goodra in XY, Kommo-o in SM and USUM, and whatnot. For remakes I use the main pseudo of the generation of the game they originated from: so my current HeartGold team has Tyranitar, while my Alpha Sapphire team has a Salamence and Metagross at present. It is quite fun to actually give myself the additional challenge of attempting to raise the pseudo-legendary from their weak base forms and middle forms, and then get the rush of excitement of having their awesome final forms to kick butt in the late game and post game. It's a nice way to give myself a bit of an additional challenge during these playthroughs imo.