I have posted in the question some players that, oddly enough, lack a "Open CD" option.
Wile not having that option, Rhythmbox and Banshee should be able to access the CD drive in the list of drives, but I will leave them aside for the moment.
(Rhythmbox should be able to display a music CD in the list of drives under the condition that a plugin is installed inside the player. After installing the player in KDE,
rhythmbox-plugin-cdrecorder are not installed by default. After installing those separately, I cannot enable the CD plugin. This is related to my KDE system I think.
Banshee too should work but in KDE the CD drive is not listed.)
See the end of the answer.
Considering the players that have this 'Open CD' option; until now, I could find that only in Clementine, Deadbeef, Exaile (at least v. 3.4), Kaffeine, KsCD, SMPlayer, VLC, Xine, Xix-media-player.
Audacious has this option under "Services" menu.
Amarok immediately shows the Audio CD in the left pane under Media sources - Local music (see image below).
Xix-media-player I shall leave aside for now. It seems a new-comer to me, it seems a pretty ambitious player that finds names in most cases, but has a lot of quirks, sometimes not playing at all on my system.
Considering finding and showing track names.
This kind of info is either present on the CD itself (CD-Text), or is taken from the internet. On that, take a look at this question.
As some players were able to access tracks names and info while off-line, this means that they can read that embedded CD info. From my experience 4 out of 10 audio CDs have that info on them, in the rest of cases the players have to look for info online.
Among the selected players, Clementine and SMPlayer have never given me the names of the tracks. This means they neither can read the CD-Text, nor access the internet to get the info from databases like CDDB.
SMPlayer can only start an audio CD, but is not displaying the tracks at all, not even with generic names in the playlist, which stays empty.
Kaffeine can find the names of the tracks in most cases (and is one of the best in this sense) and while it will not show the CD tracks in a playlist at all, it will (only) show the proper name of the playing track on the window name. I should leave it aside, but I'll keep mentioning it because it is so good at finding the proper names of tracks.
Considering the access to CD-Text (off-line info on CD tracks), the only players that I found able to read it were Audacious, Amarok, VLC, Deadbeed, Xine and Kaffeine. Amarok, Xine and Kaffeine were able to access the CD-Text on all CDs that showed that kind of info (offline) while Audacious, VLC and Deadbeef accessed it only on some CDs.
Deadbeef didn't seem to me (at first) able to fetch the info from the internet because of a bug - but that can be in fact solved by NOT checking the the option "Prefer CD-Text over CDDB" (under Preferences-Plugins-Audio CD player-Configure). More here.
To start playing a CD in Deadbeef with a command:
Considering the capacity of fetching info on the CD tracks from internet databases, the most capable seem (in KDE) Audacious, Amarok, Deadbeef, Kaffeine, Xine and Exaile. They were able to find the needed info in most if not all cases, while the rest lagged behind.
From my experience, when VLC was able to find online info on a CD that contained no CD-Text, KsCD did the same. On rare occasions these two, along Amarok, were able to find online info that was not found by any other player mentioned here, while in most other cases VLC and KsCD lagged largely behind the rest. This means maybe that they access only some more rare and/or old database that the other mentioned players (except Amarok) do not access.
Xine and Kaffeine are mainly video players (and one should be normally privileging here a proper audio-player software. Xine has a somewhat odd/oldish look and Kaffeine has no playlist for audio CDs (AFAIK).
Therefore, my favorites here are:
Deadbeef, Audacious, Exaile and Qmmp
(for Qmmp see update below), especially that they have tabbed playlists (a Foobar2000-like feature that I learned to love and cannot do without).
Amarok is good, but I find its GUI a bit bloated and often buggy. Exaile cannot read CD-Text, but that should not make a big difference these days.
Maybe KsCD can be dropped completely in favor of VLC. VLC deserves to be taken into account along Deadbeef for accessing CD-Text too.
Outside KDE, beside Audacious, Deadbeef and Exaile:
Banshee has no "Open CD" option but the Audio CD drive appears in the left pane once the CD is inserted (this doesn't work in KDE). This player is able to find internet info about the CD tracks, but its capacity is somewhat limited compared to others mentioned here. - It cannot read CD-Text.
Rhythmbox installs along with the needed plugins in Ubuntu & Gnome-based systems (not in KDE; there, the needed plugin doesn't seem to work). It is excellent at fetching online info and it can also read CD-Text offline. No "Open CD" option, but the Audio CD entry can be made visible in the left pane by going to 'File' - 'Add music', and then selecting the Audio CD.
Both these players were also able to fetch info that only Amarok, VLC and KsCD could - and other players couldn't.
These two together are a powerful and complete non-KDE solution; (and there are also Audacious and Exaile).
I will update the answer below.
Decibel is also able to access audio CDs by going to 'Edit - Preferences - Exlorer' and enabling 'Audio CD', then selecting Audio CD in the drop-down list. It cannot access CD-Text but can retrieve and save CDDB info online, just like Audacious and Exaile.
To play an audio CD in Qmmp there is the solution presented in this answer. Qmmp can access online CD database and also read CD-Text.
Dragon Player will play an audio cd with the options 'Play Media/Play Disk' but without a playlist for the cd and without access to any info on the tracks (similar to SMPlayer).