One thing that I do when I need to use multiple exchanges (especially last year when there were multiple forks to be claimed) is to withdrawal XRP. Usually XRP withdrawal fee is very low, like 0,25 XRP.
Then I consolidate XRP from various exchanges in just one, convert XRP to BTC, and then make one BTC withdrawal.
What is a little surprising is the fact that exchange platforms increased the fee a while back (to avoid to see their clients yelling because their withdraws take too much time (ie. Coinbase) But nowadays the fee charged doesn't make sense, $10 (0.001
BTC) for a transaction while you can send the same Tx paying less 5 satoshis/bytes.
You can also lose money by doing as you say, I mean the fees to trade Xcoins>>XRP then XRP<<BTC