Bingo!
If you want to have a great stereo in the same room as HT, this is how I would do it:
1) Get the best speakers you can find for your R&L.
2) Find a center that is a reasonable timbre match for the R&L. If SQ of HT is not critical to you, save some money here.
3) Buy surrounds according to your budget, but do save money here and put it into your R&L. These don't need to timbre match your front speakers very closely and you don't need any deep bass out of them (which also makes life easier if you plan to wall mount them - something like NHT Super Zeros are very accurate and light weight with no port so you can mount straight onto wall). A lot depends on your budget, but let us help you with selection ideas.
4) Use different sources for HT and music. For example, I play both cd's and DVD/BD on my Oppo player. However, I have a Toslink optical connection between the Oppo and my AVR's CD input and an HDMI from the Oppo to my AVR's BD input. This matters because the better Marantz and Denon (and probably others) have a feature where the settings are different for each input (less expensive AVR's may not have, I don't know). Consequently, when I use the CD input, I have it set to stereo and have my subs turned down 2dB fro the Audyssey settings. When I select BD, it goes to 5 channels (I have 5.2 setup) and I have the sub running 6dB hot because that is the way I like my action flicks. Technically, I guess I could use the second HDMI output of the Oppo to the DVD input and set the sub's to their audyssey settings. In that case, I would select BD for action movies and DVD for music videos. But I don't watch many music videos and when I do, I am willing to manually adjust the sub levels.
However, to your point, if you intend to use a sub, an AVR does a much, much better job of integrating it into your stereo system than the stereo receivers do.
The one quasi-exception to this is the Yamaha RN-803 which is a stereo integrated amp that uses Yamaha's YPAO system. I'd want to research it more, but I suspect it has the same bass management as their AVR's
https://www.crutchfield.com/p_022RN803/Yamaha-R-N803.html?tp=47041&awkw=367494928958&awat=pla&awnw=g&awcr=223886368442&awdv=c&awug=9010826
But, even in this case, the 803 has nothing on a good AVR, it only equals it...and you must navigate the menu systems without on screen display!