Exactly right. If you don't either release the stick's back pressure, or nudge it forward, the CG's downward inertia will pull the tail down, the wing's AoA will increase, and you get a bounce. The level-until-infinity thing sounds ok at first but it will take a LONG runway to afford such gentle contact and rollout as to avoid taking off again. Level means low AoA which means high speed. Wheel landing simply means tail off, and that might only be three or four inches off.
I used to be a flight instructor in Citabrias, Champs, Cessna 180 and 185. Wheel landings are preferred by the Cessnas when running light, since their CG is far forward, the horizontal stab is close to the ground, and trying to three-point it uses up all the elevator one has and ground effect on the stab still wants to keep the tail up. A wheel landing has to be done just right with that gear or you'll get a good bounce going and have to go around. Some operators, especially bush operators, will teach their pilots short-field techniques using wheel landings. Get the approach speed to minimum, flare very little and make contact, dump the flaps and get the tail well up to kill all lift and get the brakes on hard, using the elevator to keep the tail from rising any further. I have done these myself in all the taildraggers I've flown and it works well once one has the experience to be comfortable with it. I have landed the 185 and stopped it in under 300 feet.
I know of one outfit flying Helios that has the tail WAY up for weight on the mains, power on for elevator control and lots of brake. Can get stopped really short that way on marginal strips, and on such strips the Helio is easily able to get out again. Strip length is often less of a hassle than the tall trees that force touchdown well down the runway, and you'd better know how to stop quick.
In flying the airplane, which is anytime it is moving, we use ALL the controls to make the machine do what we want. And that includes the elevator in wheel landings.
Dan