What is the harm in applying too much current to the base of a NPN transistor when switching power?
It's a very normal operating mode to saturate your BJT transistor with more than necessary base current. The drawbacks are slightly wasted power in the base and slower than normal turn-off, but still faster than necessary for most applications. 

In general, you are better off with MOSFETs in these types of applications since the gate could be considered load-independent, save for some very special occasions and cases you are unlikely to encounter. The drawback of MOSFETs compared to BJTs here is that your digital PWM with Aurdoinos and what not tend to be very low voltage, say 3.3 V, and most MOSFETs wants 10 or so V to stay happy where your BJT only needs ~0.7 V.