If your talking loans, nearly all mortgages are conventional mortgages (or a similar defined breed defined by the feds). When you are loan shopping, your really just shopping for a broker, not a loan provider. That's going to be Sallie Mae or Freddie Mac, who in turn are backed the Federal Reaerves. That's why you'll receive a letter pretty quickly that your loan has been sold to one those two.
Your not even shopping for a loan servicer - as that can be sold and changed almost immediately too, or is already subtracted out to Mr. Cooper or someone else.
There is very little competition since it's all defined by the feds already. It's super regulated.