I am not sure what other ways there would be to actually perform this in order to profit, but wouldn't doing arb with existing balances on exchanges work in a similar fashion than waiting for the funds to be deposited?
Exactly. All the posts here are commenting about transferring deposits to different exchanges. That's not how to do arb, and of course you'll lose money like that. You should have balances in all pairs on all exchanges you intend to arbitrage with beforehand, and then do the arbitration at the exact same time (buy order on one exchange, sell order on the other with no delay). The only time you'd then transfer between the exchanges is much later when funds from one pairing have depleted, or you want to cash out a little.