Some measurements are not compatible.
The simple answer is that it wouldn't make sense to mix different types of units. For example, take
There are many reasons -- such as what your first answer mentioned. Another case is when you would be multiplying a measurement times a coefficient which has units.
An example of the case I mentioned above involves density. Density is mass/volume and is typically found in units of
Assume your data is a density with units of
I hope this helps,