Framework Laptop 16 is an unusual case. Linux can utilize MUX because MUX itself is OS-independent, but it cannot utilize NVIDIA Advanced Optimus or AMD SmartAccess Graphics because they are available only for Windows. So the problem is not MUX itself but how you control the MUX.
When laptops with switchable graphics cards started appearing, having MUX was the only way to use the dGPU on Linux because MUX controls which graphics card is connected to the monitor, and MUX toggle was usually in the BIOS, making it OS-independent. In contrast, MUXless “switching” aka hybrid mode, works by the dGPU not being directly connected to the monitor but sending the resulting data to the monitor through the iGPU, which required OS-level support. So for a long time, it didn’t work properly on Linux. I had one MUXless laptop, and GPU switching on Linux worked so terribly at that time that since then, I’ve only bought iGPU-only laptops. But from what I’ve heard, it is working quite well these days.
As Mario mentioned, sending data to the monitor through the iGPU adds latency, and I think it also prevents Nvidia G-Sync and AMD FreeSync from working. So a couple years ago, Nvidia introduced NVIDIA Advanced Optimus, and AMD recently responded with SmartAccess Graphics. The idea is that instead of sending data to the monitor through the iGPU, the GPU driver itself switches the MUX. The problem is that this currently only works on Windows, and for some to me unknown reason, Framework has decided to rely solely on this solution and not offer an alternative option to control MUX in the BIOS.
So having MUX is an advantage for a Linux laptop unless it is the same case as Framework Laptop 16.