There are so many easy plugins for various e-commerce carts and also BTCpay Server with other options for those that can install and run software on their own server it means BitPay with its fiat withdrawals which are beneficial will not be the only option out there.
I agree that BitPay is not going to die anytime soon because as said above, most merchants wants a convenient and easy way to instantly convert BTC to USD and BitPay happens to be one of the first services to provide that. However, I don't see them dominating the payment processors scene... not with the way they're currently operating anyway (enforcing KYC for buyers, trying hard to push B-cash, implementing BIP71, banning countries etc.).