There are very rational reasons to use lawyers. If the other side is using lawyers, you can be sure that they have tried to slip in terrible terms that you really don't want. They won't look that bad, but they will be bad. Relying on yourself to find them is just stupid.
And once you're using a lawyer, that lawyer will naturally be inclined to try to turn the negotiation into a gravy train.
Try this. The next time you are part of a negotiation and want to redraft the agreement, ask yourself who you are doing it for. Are you serving your client's best interests? Or your interests?
Here is another exercise. The next time you see the need to mediate between "big egos on the business side", think carefully about how those egos got unhappy in the first place. I'll give you even odds that the issue they got upset over is one that was introduced by a lawyer. Could the conflict have been avoided entirely if it was negotiated differently? My guess is that, more often than most lawyers would want to admit, the answer is yes.