That sounds onerous to me. When we started looking four years ago, we went to a few open houses and used Zillow extensively. That helped us identify our needs and wants in the way of a new place. When a place showed up on Zillow that looked very interesting but I was about to leave on a trip out of the country, we decided to call an agent we had met at an open house a couple of times and see what he could do for us on very short notice considering the home was occupied. When he managed to set up a showing for us two days after a storm dropped 18" of snow on the area, we decided to let him work for us but there was no exclusivity agreement - IIRC, he was set up as the "buyer's" agent on the purchase agreement. While he was able to show us other houses, we ultimately came back to the one I found on Zillow. After a bit of back and forth, we signed a purchase agreement for the home. Subsequently, our agent was very helpful with dealing with the issues we found with the home and working with the seller's agent to rectify them.
I guess the point I'd make is that there should be no need with all the online resources these days to depend totally on an agent to find you a home. Rather, IMHO they are more useful once the purchase process starts with handholding through to the final closing.