I disagree. The quantity of feats is intentionally small to make sure it's not the primary basis of richness and depth, and I don't even think the rules are written with a lot of multiclassing in mind to begin with. Sub-classes are intended as the primary source of richness and depth, with backgrounds another source, race and class other sources, etc.. I don't even think feats and multiclassing make the top 5.
You're conflating two things.
You can claim what the designers intended all you want, it does not change that I assert that feats and multiclassing are a big part of mechanical character complexity.
You are welcome to disagree with that, but not by talking about what the designers
intended.
If you do want to discuss actual mechanical complexity rather than somebody's hopes and wants for it, I'm all ears. In that case, I begin by saying that since feats and multiclassing are the only two subsystems that add to existing characters, they automatically rise to the top as most likely suspects.
When multiclassing then is the only way to multiply the existing content (rather than merely adding to it), it to me is clear it is by far the most enrichening subsystem of all.
I know some posters want WotC to get away with creating a much simplified game without having to answer for the much-reduced mechanical texture (or crunch), but I'm having none of it.
Without multiclassing and feats 5th edition is unbearably non-complex and I don't care whether the system is balanced without them. I need it to be balanced with them, since it's the only way I want to play the game.
But that's personal opinion. Back to actual fact.
The first step is to establish that without feats and multiclassing, this edition is a huge step backwards in crunch. Sure we have subclasses, but mechanically, there is only one big choice point (at level 2 or thereabouts). The next is to establish that since release, that level of crunch has barely increased at all.
Now, you may like it or you may not like it. But please don't muddle the issue. This isn't about what you like, or what the designers want us to like.
Best regards,