What the C++ (and C) stadards could use is a native type for SIMD vectors. In other words, standardize the GCC vector extensions [0] or some variant thereof.
Just adding a new header-only library for vector arithmetic isn't something that needs to be in the language standard (library), there are lots of options for that already (such as glm[1]).
I've been using vector extensions for my 3d graphics and physics stuff for years now and it works great. There are some pain points, but it already covers most of what I need. As a bonus, it can be used in plain C and you get all the usual math operators (+, -, /, etc) for free. There are minor incompatibilities between GCC and Clang, but nothing a few #ifdefs won't solve.
Here's a quick introduction in a few lines of code:
typedef float vec4f __attribute__((vector_size(16)));
vec4f a = { 1, 2, 3, 4 }, b = { 5, 6, 7, 8 };
vec4f c = a + b;
vec4f d = (a + b) * c; // with --ffast-math, you will get fused multiply-and-add (MAD)
In my projects, I've always put together an ad-hoc collection of arithmetic routines I need (e.g. dot, cross, matrix product, inverse, etc). A proper, well tested library of basic math operations for SIMD vectors would be very useful but I haven't got the time it takes.
If anyone is interested, some of my math routines are bundled in this github repo [2]. It's incomplete, undocumented, not well tested and there are known issues I haven't gotten around to (e.g. quaternion products give wrong results).
If anyone thinks this is useful and is interested in contributing/collaborating, leave a comment.
[0] https://gcc.gnu.org/onlinedocs/gcc/Vector-Extensions.html
[1] https://glm.g-truc.net/0.9.9/index.html
[2] https://github.com/rikusalminen/threedee-simd