Okay, we have a lot of bad advice going on in this thread so allow me to shed some light on this subject.
The PC-7424XP is not going to damage your paint unless you hold it by the cord and beat the car with it. You can't burn the paint with it and you are definitely not going to remov paint with it if you were to use it wrong as I demonstrate in these videos.
How Safe is the PC-7424XP? - Part 1
How Safe is the PC-7424XP? - Part 2
There is no way that you can duplicate the results by hand that you will achieve using a polisher. Not in your wildest dreams. There is no way that you can move your hand at the same speed that a polisher moves for any kind of sustained amount of time. Also, the PC
rotates and oscillates. When you do this by hand, you are moving in circles that are not uniform and nor is your pressure. Working by machine is far superior than working by hand.
You are going to quickly find out that you will not be able to remove those swirls by hand. Don't be surprised. Swirls need to be removed by a machine.
The process that you speak of is called claying, and it is done with a clay bar. You cannot look at your paint and see that it needs to be clayed, and you can't check by just rubbing your hand across the paint unless the paint is horribly contaminated. Wax does not protect your car from needing to be clayed, it protects the paint from oxidation. It also protects the shine that you get from polishing the paint. Wax does not make paint shine, polishing the paint is what makes paint shine.
The following video explains claying in more detail, and
this write-up will also provide you with some important information about claying.
Inspecting the Paint for Claying Necessity
You are correct because a cleaner wax actually polishes the paint. Polishing is necessary if you want your paint to shine. Just as in the military, you were never told to wax your boots. You were told to polish them and when you did, they shined like glass. This is also true for jewelty, glass, aluminum and a host of other things that you want to make shine.
You polish, not wax. Wax is a protectant, not a shining agent.
Here is my car without a drop of wax on it. I did nothing but polish the paint. Notice the depth and clarity.
Here's a Suburban with God awful water spot damage. The only thing I did to this paint was polished it. There is not a drop of wax on it. Polishing is also what removed the swirl damage. This was done with a PC and some Adam's Swirl & Haze Remover followed by some Adam's Fine Machine Polish. Both products are POLISHES.
After some coaxing...
Polish made this paint shine, not wax. All the hand polishing in the world would not have fixed this damage. OP, get yourself a PC and you will be able to work wonders like this also. When I test a guys paint with my light, I quickly see if his paint is flawless or if his technique is all screwed up.
As Jim Rome would say, "Don't be THAT guy."