It's a waste to not use an exchange if OP has already handed out their KYC info to them (unless there are other alarming reasons to stay away). Best to exhaust every option there is first, otherwise they'd be increasing their risk to identity theft and data misuse by jumping from one exchange to another every time it gets 'hard to pass'.
If OP already sends the document or fills the KYC, OP should finish it by contacting customer services and asking if his verification process is hard to complete. But I do not mind leaving the site if I have hard verification on them as many others will give easiness to their new members because they need members to run their business.
Well, I don't think users like OP would have to undergo frustrations in repeatedly submitting KYC documents, and fail every time, if they have the option to just do away with it. This is time-consuming, irritating, annoying, and so on. Nobody would really get into this inconvenience if they have the choice.
Most often, there must be reasons why some are compelled to comply with this hassle. Perhaps their funds or accounts are locked pending KYC approval. Perhaps they are trying to increase their deposit or withdrawal limits. Or perhaps they need to trade with fiat. I mean, there must be reasons why OP and others cannot simply leave the exchange.
I do not think the exchange can do away with it because once we send the data, that will be recorded on their servers. Unless we skip the process and decide to leave the site without completing the verification, they can not have our full data.
I have experienced my account getting locked by the exchange but after I communicated with their supports system, they realized that I am the owner of my account so they opened the lock and allowed me to continues using their services.