Note the difference between symbol and unit. One does not write current is 5I, just because I is symbol for current; instead, I = 5A. Similarly, Kv = 100 rpm/V, where rpm/V is the unit. KV = kelvin*volt, which makes absolutely no sense.
There is nothing messy in the symbol Kv and it follows the practice of using K for constants like this, where units are then application-specific. But it's a symbol, not an unit. If you want to be concise, just don't use the symbol at all, the unit obviously tells the reader what it's all about, just like we say "1000W heater", not "P=1000W heater" or, incorrectly, "1000P heater".
Note that SI system reuses same letters in both symbols and units. V as symbol is volume, V as unit is volt for example.