In an ideal world the raw converter rather than the profile would do the gamut compression. Then it could adapt compression depending on image content. If there are no high saturation colors, it would have no compression. No compression of course looks best when all colors fit in gamut. In high saturation no compression will yield colors that clip, and you loose details.
The problem is that raw converters don't have realtime subject-dependent gamut compression, so you have to make a tradeoff in the profile. The safest way is to put pretty strong compression in there so you get good rendering with high saturation bright colors, but this does not come for free as you have noted. In order to make a smooth transition from low to high saturation you cannot just have a sharp compression in the end (then gradients would look bad), but you must start compressing also for pretty normal saturation colors. In other words you get compressed tonality compared to the "no compresison" mode.
The difference between sRGB and AdobeRGB targets is small, the difference between Strong and not is much larger. The sRGB/Adobe mode only works on the chroma axis, while Strong adds a HSV-Value compression too to reduce clipping. The thing is that clipping is mostly due to too bright colors rather than too saturated, so the Strong has a much stronger compression effect. This is also why the difference between sRGB vs AdobeRGB targets is so small -- less happen on the chroma axis than one may think. It's not a zero difference though which one can see when studying closer.
An interesting observation is the "cheating" Adobe Standard does. The tonality in their result is good I think (Almost as LRPD AdobeRGB-Strong close to clipping, and perhaps a bit smoother in clipping), however partly by putting lots of green into reds making them more orange. This way you get less clippy bright reds, and more stability when clipping, at the cost of incorrect hue. Pushing hues towards green is a common method made in many commercial bundled profiles, not just Adobe (makes it possible to make brighter colors with less and more stable clipping). With Lumariver Profile Designer the goal has been to not cheat with the hues though, which makes the compression task a bit tougher. There's still a small cheat with the hues with LRPD too, with strong clipping reds you will get a shift towards orange, this is needed to make subjects like sunsets look good, some more tonality is also retained.
The default is set to "AdobeRGB-Strong" and that is what I think most people will think is the best tradeoff if you're making only one profile. However, if you have the possibility to change profile depending on subject, having an extra profile without compression is a good idea, so you would use that when there's little or no clipping issues, then you get better tonality in medium-saturated colors.
If you go advanced and get into tuning hue errors in the optimizer you could also look into pushing reds towards warmer rather than cooler (if that's not already the case), this adds some extra stability.
I have worked a lot with the gamut compression algorithms, and I may be doing even more work with it in the future. There will always be tradeoffs though, which is in a way what makes profile-making fun, and also what makes it valuable to have your own profile designer and not just relying on pre-made profiles by someone else. I've personally been using AdobeRGB-Strong compression, but I'm more going towards using "no compression" for subjects that don't need compression, and as my personal shooting style is pretty low on saturation that makes up 90% of my pictures. Would I shoot a lot of colorful flowers though, I'd use gamut compression all the time.
Sliders in the raw converter also allows you to manually control the gamut a bit, then one should generally first try to reduce brightness/lightness rather than saturation of the clipping hue. But then you need to do manual stuff per image. What suits you the best depends on what type of subjects you shoot and what type of post-processing you do. The all-around "just works" mode I'd say is the defaults "AdobeRGB-Strong" though.
I hope this helps.
(Oh one more thing -- I should say that gamut compression in camera profiles is not like gamut compression (or rather gamut mapping) in printer profiles. In printer profiles you map from one fixed gamut to another fixed gamut. In camera profiles you don't really know what colors you're going to get ("cameras have no gamut") and also the output gamut varies, so less exact, more perceptual and less mathematical methods need to be used.)