I'm not convinced it would. The crypto community on a whole mirrors the general population on the whole, and there are far too many naive newbies or just idiots who do no due diligence around. "A person is smart. People are dumb."

Binance hacked for $40 million and hacked for users' KYC data - continues to grow as one of the biggest exchanges in the world
Coinbase hand over details directly to the IRS and US government, sell users' private data to third parties, develop software for tracking users and rent it out to the FBI/IRS/DEA, insider trade - continues to grow as one of the biggest exchanges in the world
Huobi are running a fractional reserve and using customers' deposits to invest in high risk products for their own gain - continues to grow as one of the biggest exchanges in the world
Bitfinex printed $800 billion Tether out of thin air which they loaned to themselves because they are insolvent - continues to grow... you get the idea

Any exchange caught out by proof of keys (as Quadriga was), will just freeze withdrawals, come up with some excuse, and then go back to business as usual the next day. Any customer smart enough to ditch an exchange caught out by proof of keys is smart enough to not be storing their coins on an exchange in the first place.