The answer to your question is yes, and no. First discs are the gold standard for video, and the higher end players have the edge here.
For audio, the PCM is sent over HDMI and AVRs will decode this, and I think this is the way most do it.
Things get messy with SACD and its DSD. Not all players will send DSD over HDMI, and not all AVRs will decode DSD. Players that can send DSD over HDMI can be set to convert it to PCM to be sent over HDMI to units that can not decode DSD. All this upsets the audiophools, but they are too ignorant to realize that no one edits in DSD anymore, as it is such a huge PTA. So DSD recordings are converted to PCM for editing and processing, and then back to DSD. This is all because audiophools refuse to educate themselves about digital audio, and believe long standing misconceptions about it. It for this reason DSD refuses to die, which it should, and will eventually.
We would be far better off with audio only BD. That would allow more channels, and be better all around.
I will confess that I do still use a CD player in my theater system. The reason is that darned CEC. I need that to use some apps in the TV and send the audio over eARC. I use my HTPC mostly, but for certain sources the TV app is best. However when you turn on a player the TV turns on. If you turn off the TV it turns off the player.
The only way to prevent this is turning on an off CEC. That means finding menus, and it is a pain. So I just find it easier to use a CD player.