I've been using a cleaner (aka polish) wax, then moved to synthetic wax/sealant for decades, ever since vehicles switched from glass.
It does not last as long as clearcoat. The ease in application and no degradation of clearcoat later, more than makes up for it IMO.
No problem from heat, natural wax will get much softer, I suppose in theory it might pick up more road grime in very hot weather but if you have the road grime, and you are waxing the rest of your paint too, the whole vehicle needs washed at the same rate. I'm not implying to use (same) cleaner/polish wax on the whole vehicle if you have a pristine clearcoat on your paint, no benefit then to abrade the clearcoat, unless it's got residue you can't get off otherwise.
A strong wash solution, whether at a carwash or DIY, can strip off headlight wax, or your entire vehicle wax for that matter. Fortunately it only takes a minute to put more wax/sealant on headlights. Rewaxing the entire vehicle again, not so much.
When I go to a self service car wash, I take a bucket and tiny bit (just enough to get the job done) of car wash soap with me, only using their rinse setting to make a wash solution, not using their foam cannon. Automated car washes with the rotating brushes, only for my older vehicles that have no shiny (especially not piano black!) plastic to swirl up and if you put clearcoat on your headlights it's not good for that either. It's not even good for a bare, new headlight with nothing on it. Abrasive cleaning anything that doesn't need it, is bad for the surface... though in some climates, it beats having salt sit on the vehicle if you don't want or have other ways to get road salt off.