Just read through this thread, here's my two cents...
Modern
quality compounds, (there are still caveman compounds on the market), will finish down to almost perfection.
I would also say don't be fooled by the finished appearance after compounding with an aggressive compound and aggressive pad, (foam or fiber). The results may look good but if you were to wash the car with a strong detergent soap to wash off the polishing oils my experience has shown me you'll see dull, hazy areas BECAUSE you used an aggressive compound and an aggressive pad - both can scour the surface and remember, for most of you the surface is a scratch-sensitive clearcoat paint.
You might only see the dullness on a black car but if it's happening to black it's happening to all colors your eyes just can't see it.
My own practice and my strong recommendation is that if you start with an aggressive compound and a cutting pad then at a minimum you should either follow this with a secondary step using a finishing polish and either a foam polishing pad or a foam finishing pad and then go to your LSP.
Another option would be to follow with a quality cleaner/wax like McKee's 37 Jewelling Wax. Been there done that and works great.
Also if you look at all the show car detailing we did at my last class, each of these were 3-step or 4 step processes. Aggressive compound followed by finishing polish followed by LSP. For three cars we compounds, polished, the stripped and the applied a ceramic coating, so that's 4 steps. Keep in mind these are all streetrods, muscle cars, classics or show cars, not ordinary daily drivers but the same principals apply to anything you work on.
Pictures: May 2016 Competition Ready 3-Day Detailing Class with Mike Phillips
I also explain why to make it a "Best Practice" to follow an aggressive compound with a less aggressive pad and polish to avoid returning to your customer a car with dull hazy paint under the oils and wax.
Again, don't be fooled by the glamorous appearance results from high quality compounds, I agree they look GREAT and even tell a story about how I called RUPES after using Blue/Blue on a yellow 1956 Nomad that's on the cover of my RUPES book and even though the results from Blue/Blue looked awesome I STILL followed this with White/White and then the LSP.
While the paint looks great after applying the Pinnacle Souveran Paste Wax it seriously looked great after cutting with the coarse Rupes blue foam cutting pad and the coarse Rupes Zephyr Gloss Compound. It looks so great that just to make sure the RUPES official recommendation to follow their compound with one of their less aggressive polishes was correct I double checked with RUPES and they said "yes". (No telling with these crazy Italians).
This Nomad is on the cover of my RUPES book and I detail all the cars in my how-to books.