We all agree that in a powered aircraft, we have a pitch attitude control and a power control. It sounds as though many people posting here are desperately trying to figure out how to use them in isolation - use 'em together! Co-ordinate the control of the aircraft in the pitch axis, as you do in the roll/yaw axis during a turn!
What has little illumination in this discussion is which side of the power curve you're on while you're doing all of this, and, the configuration.
NO, it is not always prop wash only which affects lift with power. Application of power does not always result in a pitch up - I have a power plane which does neither, but it still flies entirely normally, and follows all the "rules" of stability and control on both sides of the power curve. People's minds are fixated on Cessna/Piper, which are examples of these relationships, but not the only examples of how pitch and power affect each other in flight.
Let's extend the thinking farther ahead... Helicopters:
They have a cyclic control, which can be used at any airspeed to lower or raise the nose. They have a collective, which can be used at any speed to increase or decrease lift (let's assume it's a governed engine, so collective equates to power).
If you're hovering, you've increased lift to get there, but not used it all (I hope), and could raise the collective more to climb. But you're not doing that, you're just hovering. You push the cyclic, nose dips and you move forward = speed increases. So far so good? but as you increase speed, you increase drag, and because you have not further raised the collective, you give up some power to that, so you're going to descend a little. But it's okay, you lifted off a skyscraper helipad, so you've got altitude to loose safely. So far, everything we have done is behind the power curve and in helicopter terms, slower than translation speed. Roughly speaking, collective (= power) is primarily controlling lift, and cyclic (= pitch) is primarily controlling speed. Some co ordination of these with the other control is nice, ut it work without.
Then, speed increases, like magic, you pass through translation, the nose pitches up, and you further lower the nose (with the cyclic). So far, you could have done all of this without changing the collective (power), though there would have been some altitude excursions.
Now, through translation, and in cruise flight, still with the same collective power setting, if you want to climb, you will increase pitch with the cyclic, which is now primarily controlling lift (climb), though you'll have to add collective, if you want to maintain the same speed. If you want go faster, you will raise the collective (increase power), and you'll go faster, though you will have to lower the nose a bit to not climb, so collective is controlling speed.
When you approach to land with power, it all reverses, you descend in with low power, on the fast side of the power curve, but as you slow to enter the hover, you're going to have to add a whole bunch of power, and pull the cyclic back to prevent a pitch down. You just translated through to the back side of the power curve. You'll have to add move of both pitch and power to actually slow to a zero speed zero descent hover, but collective is doing lift, and cyclic doing speed again. If you're not sure, pull the cyclic back, and you'll go backward.
So why have I explained flying a helicopter in a primarily fixed wing thread? 'Cause it is surprisingly similar, though the plane will mask the effects pitch/power effects with stability, which the helicopter really does not have much of.
You will find in some flight manuals (some C 150, for sure) contain instructions for landing the aircraft with no pitch control (the cables came off the elevator
). When you read the instructions, and do what it says, it works (but for heaven's sake, do it with a really sharp safety pilot!) You will not use the elevator at all ('cause you broke it), and you will not use the trim or flaps to change pitch in the last phase of the landing, power only, and it works. While you're carefully using power, the speed of the aircraft is not rapidly changing, but pitch and lift are.
However, after all of that....... If I were flying with a pilot who was thinking their way through this while flying the plane, and mechanically selecting one control input then the other to fly, I would be taking them aside for a long talk after landing - 'cause they don't get it yet.
I would expect any self respecting Cessna pilot to be able to extend electric flaps, and change power with one hand, and control the pitch and G with the elevator with the other hand, in such a way that there was the desired pitch change as you slowed, but no G change at all. This would demonstrate appropriate co ordination, and be evidence that that pilot need not worry about which control does what, they can use them appropriately unison, and it does not matter!