"What's Stopping Someone From Buying From one Exchange, Selling in Another?"

Nothing

Although, as others have mentioned, the high price of coins now has made the fees enough to kill any profit potential.

Back when coins were $4 each, you'd only incur a fee of less than $0.03 per transfer, which means buying at $4 (anywhere) and selling for $5 (anywhere) would make a nice profit. But at $120/coin (at the time of writing this) you will incure a fee of $0.72 per coin per transaction, which means you'd need a gap of more than $1.50 between your buying and selling prices to see any return. It's possible to find a gap that large over time, but not between exchanges with an immediate buy-sell maneuver