... is there any reason NOT to use tether and streamline the process?
Does Coinbase support withdrawal through BSC network? If so, you can do it that way. You would need both BNB and USDT (BEP-20) to buy on BSC AMMs/DEXs though.
Just an FYI that in most platforms, USDT are converted back to BNB or WBNB before it's swapped to any BEP-20 token. As a result, the transaction fees could be higher compared to buying with BNB directly. Good thing the added fee is minimal on BSC.