Transistor biasing, Large Resisor values
Two drawbacks come to mind:

Firstly, noise. Two kinds really, thermal noise and shot noise. However, if the transistor is being driven into saturation, noise performance is probably not in your list of considerations. If you were making a linear amplifier however, it could be.

Secondly, switching speed. The base is not without capacitance. The Miller effect effectively amplifies this capacitance. Driving the transistor hard into saturation results in storage delay. There are various methods to reduce these slownesses, but all of them are made more effective by driving the base with a lower impedance, which a resistor in the megaohm range isn't. However, slow may not be a problem for your application if slow is fast enough.