In theory there are some advantages like being able to leverage larger stacks against each other in multiway pots. The game is also more simple, the shorter your stack and you limit, how much you can lose at a time. So if you struggle with things like how to play 3-bet pots or handle postflop raises, then you can avoid some tough spots and potentially costly mistakes by buying in short.
The flip side of that is, you also make the game easier for your opponents, and you limit, how much you can win from an opponent in a single pot. So if you are a winning player in your game, you kind of handcuff yourself and limit your potential winrate by buying in short. You also force yourself to either play with widely different stacks or constantly find new tables, every time you have dubbled up.
10-15 years ago short-stacking (10-20BB) and cap-stacking (40BB) was quite common in online cash games. But these days most sites have raised the minimum buyin to 40-50BB, which has completely removed short-stacking as a strategy. You still see a few regs cap-stacking, but in my opinion they are typically kind of bad regs, and its not something, I recommend.