EA doesn't get paid unless it goes through so this is a daft statement. However some are awful for very different reasons I agree. You, the buyer are paying the solicitor not the agent so perhaps you should hound them instead.
I sort of agree - the logic should be that the EA doesn't get paid if it doesn't complete so they have motivation to get things done. However, in our recent experience our EA were more interested in getting new properties on the books than helping us with our sale. Mathematically I guess it makes sense, add ten new files on for the risk of one falling through - or that is very much how it felt to us.
As soon as we exchanged the communication from the EA dried up, calls not returned, messages not passed on, our sales "progreser" always out doing new valuations.
Our solicitors on the other hand were brilliant, they couldn't do enough to help and were always on the ball and ready to assist.