But it complicates the compiler, complicates the tools, complicates the error messages,...
Take something as "simple" as operator overloading. If a beginner does a "5"+5, the compiler is forced to respond with "no operator + for the types given, types are: int, std::string" instead of the infinitely more friendly "can't add string to int". I actually _like_ operator overloading, I wish more languages stopped the silly practice of making language-provided primitives somehow sacred and closed-to-extension. But look at how even this relatively straightforward and useful feature ruined the error message.
Part of this particular example is bad error message design. I mean, what are the chances somebody intended to do operator overloading but then forgot to implement the method? It would have been much better to say "Can't add string to int, Did you forget to implement operator+(.. .,...)?". This centers the common case first, then reminds the experienced about what could have happened in their case. But even this might confuse beginner and convince them that "5"+5 is somehow a reasonable thing to say (because it actually is in some contexts) that they just need to get that fabled operator+ from somewhere to make it work, instead of just outright telling them " nonsense, not gonna work".
Extensions are always, inherently, abstractly, a tradeoff. Because even if you are a perfectly spherical coder who doesn't interact with other code in any way, you at least interact with the language tools. And the tools _must_ know all the of the language: instead of just having the luxury to say "sorry mate can't do that" when encountering "5"+5, the editor/IDE/compiler has to spend the cycles to see if it _can_ do that, then report a message that simultaneously says that you can but can't. As the features accumulate and interact, the tradeoff curve increasingly inflect against adding new things.
All of this in the abstract is a fairly balanced argument that applies to any language, the particular case of C++ is much, much worse. C++ have this aweful way of "retconning" new features. I can never put my hands on it, but C# creators practically design a new superset every major version and call it the same name without ever making people angry or afraid that the language is spiraling out of control, but every C++ feature gives me this dark feeling of "is this never ever going to end? how far are you willing to take it?".
Part of that is undoubtedly the syntax, remind me again what language class (regular, context free,..) is C++ syntax? The other day I was fooling around and thought of adding discriminated unions to C++, just a thin syntax layer over a more verbose idiom. The very first thing is to parse the damn thing, but that way lies madness. Because C++ have no agreed-upon, guaranteed formal grammar. There is a grammar online but it's gargantuan and was written by one man, there is a grammar in the standard but it's gargantuan and the standard says it's there for illustration only, there is a grammar (implicitly) in the source code of any working parser but it's gargantuan and full of hacks. So for all practical intents and purposes, C++ has no formal grammar. Think about that for a minute, a formal language that has no formal grammar. It's the bare minimum any formal language can have, and yet you can't do it safely because of the massive, beast-like bloat that is that language.