KYC might be necessary when dealing with huge amount of bets. I personally haven't tried it, but I've heard some of the trusted gambling websites are doing this.
There are some online gambling websites that uses fiat that doesn't require KYC, you only need to deposit money from your E-wallet to their website. That's the same as depositing your Btc from your wallet/exchange to their website, and that makes you less anonymous.
So, most probably both crypto and fiat sportsbook will co-exist and none of them will be replaced by either solely crypto or fiat.