My guess would be that BitPay requires the 6 confirmations, not NameCheap in particular. If they wanted to accept zero confirmation transactions then they'd likely need to implement their own Bitcoin wallet and associated checkout service.

The appeal of a service like Bitpay of course is that it converts that Bitcoin into fiat currencies, such as the USD, without the vendor having to deal with it. I agree that a zero or single confirmation system could be implemented by a vendor such as NameCheap. However, it would be more costly and time consuming than their current use of Bitpay.