Is there really any advantage of going with one mortgage broker over another, or on particular bank over another, for a real estate loan (as long as the service is good)?

Yes. Brains, experience, lender relations which help pricing, speed of processing, etc.

Get comfortable with someone or an online relationship is ok too! I have not met directly with a customer to take an application in about 5 years. It’s commoditized to the extent that Fannie, FHA, VA, etc. have guidelines and buy all the good mortgages.