I have at least $500.00 in sandpaper in my shop. That includes a lot of aluminum oxide, carbide and 3-M flavored stuff in rolls, hook-and-loop pads, and sheets. If I don't count siding sanders, grits range from 40 to 3,000, or higher, if you include the granite working stuff.
Add to that, I have jars of cerium oxide, chromium oxide, diatomaceous and so on. Then there are my various commercial buff compounds in sticks and liquids.
So, I agree. We have a metric ton of choices. However, the polishes I make up cost me a fraction of what, for example, the Festool disks or diamond polishing pads do. Too, they get into crevices the papers and cloth sand pads and such cannot.
Fine sandpapers and such load really quick and you can't use them with water or oil. On the other hand, loading a cloth or paper towel with compound is the game you want to play.
On removing the polish before applying finishes, it sounds like a good excuse to learn something, and to test reasoning skills.
For example, paint thinner, turpentine, delemonine and Naphtha all work to dissolve toilet ring wax and real bees wax and keep them fairly well suspended. Since these thin polyurethane too, it would stand to reason there is a good probability the poly would play well with an item polished then cleaned of the polish using a fresh paper towel or rag. Even more so, if cleaned with a cloth dampened in a solvent.
Then there is shellac. I haven't tested the "wax" with alcohol. Denatured or other. I use a lot of it though, both as a sealer and a quick and simple finish.
Think of shellac as kind of like Kilz, sans the pigment and binders.
I consider it so useful, I keep a jar of alcohol with a well used chip brush in it, next to a couple quarts of Zinsser (amber and clear) on my work station. When something needs a quick finish, I lift the brush, smack it against the insides of the jar, dip it in shellac and go for it.
Finally, there is the friction polish approach using shellac, linseed oil and alcohol. It takes longer to build coats on an lathe project, but it works too.
If these things don't work, it's only because you left five pounds of polishing compound on your turned item.