I do the same and I also play with deposited money of my own but since stake is well known to have whales at VIP levels IV which have wagered a huge amount for these persons sure they need KYC and proof of income as it is natural for any entity,in this case stake casino to have doubts that maybe money laundering is taking place through their website and they don't want to have legal problems with the law because of such happenings.
Most likely these whales always have a solid proof of income verification which entitles them to keep playing there at these high levels,some wager more than 100.000 dollars daily there so for this it is an absolute necessity to have proof of income.
VIP Level can be achieved without being a whales, means that VIP level IV is not always a whale. Some normal people can reach this level within years by betting small amount as long as they play regularly. Imo Proof of Income verification has nothing to do with VIP level, it is more about how much a players spend (deposit/withdraw). A new user can be asked to verify proof of income if there is something suspicious. By the way, looking at the list of accepted document for proof of income. I my self believe that I can verify proof of income because I own betslip, but I will never do it because I do not want to reveal my real name, the company name where I work, etc.