I do think you rightly have a valid concern about adding more new systems to the game. Where I would push back, however, is that, in general though not necessarily with you, this point is not evenly applied, but often restricted to psionics.
Some probably do, though its also possible that people don't like psionics for reason other than the addition of a system.
Although we may say that all casters cast spells, there are different systems and substems at play. The warlock casts spells, for example, but pact magic operates differently than a wizard or sorcerer's spellslot spells per day system.
You'll be gratified to know that neither warlocks nor binders have ever been a part of my game.
Likewise, the monk does not operate off of spells, but has their abilities, including spells gained from subclasses, fueled by their ki points. We already have multiple concurrent magic systems in the game. (The artificer will also be adding a new system to the game via their infusions.)
Well first, that attribute of the monk is a fairly new one. Older editions did not treat monks as spell-casters. And yes, I dropped monks from my game back in 1e.
I believe a lot of these concerns have been addressed in the 3.5+ editions. (And it sounds that 3.5 and Dreamscarred Press's take on psionincs would serve your purposes best as they more concretely address these points that you raise.)
I would say that 3.5 edition psionics is probably the best take. But as I said before, I'd only actually use those classes if I dropped the more usual magic using classes from the setting.
Here is another set of presumptions that I find contentious, namely that (a) psionics are incongruent with the pre-existing magical systems...
Once being a 'psi' became a class that could be trained, it became nearly impossible for me to explain what it was that wasn't already covered by a magic-user. Psionics are 'mental'. So is wizardly magic. Psionics discipline their mind; so do wizards. Psionic power arises from within the self, and so does a wizards or sorcerers magic. Psionics are either native talent or learned. Depending on which is true, how are they fundamentally different from wizards or sorcerers?
and (b) that the magical system is presmed as "coherently explained," which is a particular sentiment that may be far from universal or true.
I'm sure the sentiment is far from universal. Many DM's I've met have never even been able to explain why wizards memorize spells and then can't cast them again after they do. It is just the way that it is, and they don't understand it, and many probably think it's just a stupid way to achieve balance.
For me, D&D does not present a coherent magic sytem. The distinction between divine and arcane magic, as is often the case, is one of those D&Disms that I personally find incoherent.
How is it incoherent? The distinction between divine and arcane is one of the most straight forward in the game. Divine casters draw their power from outside of themselves. Their magic is gifted to them by some inherently magical being. As a consequence, many divine casters can lose their magic if they offend those magical powers and thus they often have expected behavior they must conform to. Arcane casters on the other hand develop power within themselves, by disciplining their mind and long labor in study of the secret ways of the universe, or else by drawing on secret wells of arcane power hidden in their heritage. Are their classes that have blurred this distinction? Probably. But they've never been a part of my game, and would be rejected if they appeared to have been assigned 'arcane' or 'divine' arbitrarily or purely for mechanical reasons.
The arcane/divine divide explains in a very simple way, even though they use basically the same system (spells divided by levels and spell slots to hold them), different classes have access to different powers. Much of the perceived incoherence has to do with people making assumptions about how things work that aren't part of the system, for example assuming that clerics use their faith to make miracles - something not a part of the system at all, and from my point of view wholly incoherent when applied to D&D.
I can at least sympathize with your distaste for psionics from a similar perspective of my distate for the arcane/divine magic divide. The simulationist in me would prefer a more universal magic system.
A universal magic system would make sense if there was only a single source of magical power, and in turn would suggest that there is only a single spell-casting class. The arcane/divine divide suggests at least two sources of magical power. For my part though, for some settings, I might go down to a single spellcasting class, joining to the arcane/divine divide at the point it most closest resembles real world magical traditions (which for lack of a better term we'll class the 'occult' tradition). For 3.5, the class I'd almost certainly choose as the one universal spellcaster would probably be the Green Ronin shaman (or if I was playing 5e, a class I'd homebrew from that model). However, I can imagine settings where I'd adopt the Psion as the one universal spellcaster, particularly if the setting didn't have a lot of occult elements (usually non-animist settings).
But the arcane/divine divide has a basis in real world magical tradition, particularly during the medieval/early modern era that D&D draws on, when distinctions were made between magia, goetia, and theurgy. It also supports D&D's iconic priest/wizard divide, albeit the D&D wizard has no real basis in ancient/historical magical tradition and is a wholly modern creation (almost to the point of being a D&Dism), and if you had to pick one or the other to represent how people actually believed magic worked, you'd be better off with the cleric. Nonetheless, the D&D wizard has been so successful and iconic, that it pretty much has defined 'wizard' in people's minds ever since then.