Fees of sending USDT is pretty cheap on any blockchain besides Ethereum which will cost you like $5-10 a transaction on a good day. Unfortunately a lot of exchanges doesn't support USDT withdrawal on other networks besides Ethereum.
Also the fee on Omini later is costly also on Ethereum network like you said.
Zero fee on Algo network
$1 or less on Tron network
$1 or less on Solana network
$8 or less on BSC
Very less on some other networks too.