You can search for homes online by yourself. Most buyers do that these days.
Here's what you want to think about: Who are you going to call when you find something you like? If you always reach out to the listing agent, you're establishing a relationship with them and making it difficult for you to bring in your own representation later if you want to buy that property.
If you're in a competitive market (and an awful lot of us are), you are way behind the ball if you're waiting until a house is on a public website to a) find it and b) create a relationship with the agent who will represent you.
It is hours to days before a house hits the various public websites. That gives a buyer relying on their agent's MLS feed a huge advantage in getting into a house immediately and making an offer. Additionally, agent-only "coming soon" pages on Facebook are huge now and give buyer's with agents an even greater advantage in knowing what's about to hit the market so they can pounce early.
I cannot think of any reason why you're better off working alone at home with the internet than having a professional helping you.