For that reason, it didn't seem like a good idea to build C and C++ standard libraries, ship them with your code, and link them at runtime: The standard libraries are quite large. Furthermore, Emscripten doesn't have a single ABI, it has several code generation modes, as one example there are two typed array modes and one mode without typed arrays, and code compiled with one is not interface-compatible with another. Not having a stable ABI lets us generate more specialized and efficient code, but it is another reason for not shipping separate linkable standard libraries.
Instead, when compiling code with Emscripten we build the standard library along with your project's code. Everything is then shipped as a single file. This gives the advantages mentioned before: Smaller code size since we know which parts of the standard library you actually need, and faster code since we can specialize both the standard library and your own code, not just your own.
However, there are two disadvantages of this approach. The first is that combining the standard libraries with your own code means they form a single "unit". When normally you build your code and then link to the LGPL-licensed GNU standard libraries, it's clear that your code does not need to comply with the LGPL (you just need to comply with the LGPL regarding the LGPL'd library itself). But if you build your project together with the standard library, intertwining them in an optimized way, it is less clear how the LGPL applies here. I actually don't think there is a problem - it seems equivalent to the former "normal" case to me, despite the differences between them - however, I am not a lawyer, and also it is better to avoid any possible confusion and concern. In addition, even if the LGPL still applies just to the library, you would be shipping the library yourself, meaning you need to comply with the LGPL for it (which I don't think is a problem myself, but it is a concern for other people). For those reasons, Emscripten doesn't include any LGPL code. That ruled out using the GNU standard C and C++ libraries, which would otherwise be the first choice because of their familiarity and compatibility with existing code.