This is really just a method to verify control over assets. It’s a spectrum and third party verification is simply more reliable for this purpose. That + repping ownership is the same process they’ll verify cash reserves held in a bank account, and will ignore “cash” you might rep to own under your mattress. “Maybe it’s yours/ maybe not… put it into a verified identified account in your name to demonstrate control and that’s good enough for us”. Once it’s counted toward reserves, it’s unlikely there’s any requirement to keep it there once the mortgage is issued.