You'd typically need some kind of energy flowing into the vibrating structures, so the stabilized supply electronics need to present, anyway.
Since the currents involved are very small, it's highly desirable to place these in the same package to avoid much larger noise currents from external traces.
The signal of interest is most of times "coupled out of" these stationary supply signals. So, that coupling electronics should be close to the MEMS element, too.
Then, you've got a weak signal. You'll want to amplify that as close as possible to the source. So, in the same package, if not even on the same die.
Whenever you amplify something, you want to limit the bandwidth – to not amplify more noise than signal. So, typically, loopback filters are integrated. That's often the first thing that "leaves" the sensor: you'll find MEMS sensors where you can set the bandwidth with an external capacitor.
So, MEMS technology is exactly interesting for the opposite reasons: it's possible to integrate signal conditioning, and so you do.
If you circumvent that (for example, by replacing the external filter capacitor with an open end), you'll simply not get any sensible signal, because the phenomena observed are much smaller than what's easy measurable from afar.
That is not to say it's impossible to do that externally, but you'd have to do very careful (and potentially expensive) board design to protect these signals from noise influences, and to protect the sensor element from loading.
