Most of the time, it's just to try and delay the withdrawal.
Sounds convincing. The big question is, why would these gambling or casino websites ask KYC only if a player win big amount of money, why they didnt ask KYC before a player can proceed to play in their website. Im thinking there will be another reason for that aside from just delaying the withdrawal.
They can delayed your withdrawal indeed since you need to process the KYC procedures, it take some time for verifications and approvals, I'm also confused why this happen after you tried to withdraw bigger amounts, how about splitting it in a small fractions, are they gonna ask for players to
complete the process or they will allow if you will just withdraw little by little?
I have not tried to withdraw nor gamble huge amount of Bitcoin from any of the gambling sites. As per the OP's concern he clearly stated that these gambling sites listed above ( I know some of them are trusted and has a lot of players using their websites ) will ask KYC verification to enable withdrawal procedures for large amounts. So, I assume small fractions doesnt require any. I have never personally experience withdrawing huge amount, since I only play for micro betting.