There is only one interrupt that just happens periodically which is the timer one, and it is usually repurposed to game's own tasks. It doesn't matter what games don't call the original handler (Pinball Fantasies is one such, which also maxes out the mixer), only that there are games that don't making it not an universal solution. Some games also mask out all interrupts they don't need such as Tyrian 2000, which for example breaks SW20PC sound card's MIDI emulation as the emulation IRQ is no longer seen by the TSR. Sonud card's own IRQ is always fully hijacked and games assume there is no original handler that could be called so it isn't an option either. Keyboard interrupt is often hijacked without original being called, i.e games where CTRL+ALT+DEL or other global shortcuts not functioning.
The effect of the hijacked mixer results in stuff such as music (FM, MIDI) being too loud or too quiet in relation to other sounds, or stuff like excess noise as line in and/or microphone inputs got enabled and maxed.
Performance concern applies especially to the XT example, where every cycle does matter. It is also unknown what effects will the periodic mixer access do, I wouldn't be surprised that it will upset the DSP when timer fires between DSP accesses etc.