Most online wallets will ask you for KYC and other such requirements.
I never know that online(web?) wallet need KYC, even blockchain doesn't need to do KYC to use it, except for exchange.
If you mean 'exchange wallet', that thing is not good to hold coins for long time.
I guess he is referring to Custodial wallet (for instance- Coinbase). Non custodial wallet doesn't require KYC for storing fund. But for Custodial, I guess KYC is needed for using it for beyond the limit. Coinbase has limitation on NON-KYC accounts. You can send certain amount of BTC without KYC and will have to go through a lenghty process while with KYC, you are free to send big amount as well.