The problem is far more complicated than that, unfortunately, and differs depending on the graphics API used - Opengl, Vulkan, DirectX. The shaders are in most cases just text and can only be converted to valid executable GPU binaries for a specific GPU driver and GPU card combination - which inherently provides the digital signature that signs pre-compiled binaries, which tries to ensure you aren't loading a binary into the wrong GPU, or the right GPU that has the wrong memory mapping or API bindings/features from a newer driver solution.
Covering all GPU/driver combinations the user will have - in advance - on open platform hardware and preparing all solutions in advance isn't in the scope of PC devs, and especially when providing pre-compiled shaders at all increases the risk of hacks against the game for decompiling by exploiting a bug in these pre-compiled shader binaries, so it is always safer to force recompilation at run-time - on the CPU via the driver.
Vulkan provides an intermediate assembly language style shader intermediate format called SPIR-V which is faster to compile at run-time than GLSL (or DirectX HLSL) which are effectively text and need to do the lexer, parser, etc before being converted to the graphics driver's SPIR-V equivalent, but still needs to provide new binaries for every change of GPU/driver combination, so still favours run-time compilation for simplicity, and despite the improved stage reduction of compilation still struggles with the sheer volume of shaders (maybe 1 per material per model and maybe multiple per model per scene) needing compiled just-in-time.
Despite the slower shader compilation rate on OpenGL(and typically lower frame-rates) compared to Vulkan, the less-lean-and-mean OpenGL drivers hide frame-stutter much better with automatic algorithms that developers have to forego by using Vulkan, so the stutter might not always be from compilation issues, but from struggling to re-implement the algorithm benefits of using OpenGL that are absent in Vulkan to provide the developer with more control AFAIK.