But generally speaking you are correct on one count; the generals never wanted to attack Lee. It was the constant interference from Lincoln that finally allowed the army to rotate through enough commanders to find one willing to attack and win the war (Grant). Had he left it up to any of the first 4 or 5 commanders to prosecute the war, the north would have lost.
Actually, Lincoln finally found a commander that was willing to pour as much cannon fodder into the fight, until the Confederates expended all their combat power. Grant had a population of 20 million to draw on, plus a seemingly endless supply of immigrants who signed their citizenship papers, right after they enlisted in the army; that seemingly endless supply of manpower was Grant's only real advantage.