That's not the whole story. Litecoin has about the same theoretical capacity as Bitcoin Cash and one huge advantage for BitPay's business model: generating blocks at 4x the speed means it's more likely that transactions will confirm within the window they're willing to lock in a price for. (It's also on more exchanges, as I recall.) There's obviously some other reason besides transaction capacity for Bitcoin Cash to being chosen here.

Also, Bitcoin Cash had the annoying antifeature of using the same address format as Bitcoin, probably because it pretends to be Bitcoin, which means it's easy to accidentally send Bitcoins to a Cash address and vice-versa. Even experienced users seem to screw this up occasionally. (This certainly wasn't for reasons of wallet software compatibility; changing the address version number is trivial compared to the other changes required to port even a lightweight wallet.)

BitPay's workaround for this is apparently to use their own address format for Bitcoin Cash which is incompatible with most existing wallet software ("the BitPay and Copay wallets' BCH address format"). Non-BitPay wallet software seems to have backed a different, incompatible new address format as the solution to this problem. Of course, all of the wallet software is still going to happily let you accidentally send Bitcoin Cash to the Bitcoin payment address... it's only sending it to the correct address that may not be supported.