It didn't save the x87 FPU registers either, however a task switch set a flag in MSW / CR0 that caused a trap on the next instruction using these registers. The idea is that they are used infrequently, so it's better to only switch the FPU context when required.

This is no longer so true today, however the Linux kernel for example doesn't use any floating point or vector instructions, in order to avoid having to save these registers on every system call or interrupt.

The real inflexibility was scheduling (see my other comment)