That's begging for even more variability, i.e., any number from 1-10 for your example. Not that that would be a bad thing...
The problem comes from the interaction of damage and range. Ultras fire at a higher rate, yet they GAIN effective range, this is contrary to the performance in the proposed idea-which is that the drop in range is because of the higher firing rate. (Something you can actually, if you live in a place where you're allowed to own firearms you can test by comparing the benchrest range of a semi-auto firing slowly, with one firing quickly. the bullets go down range the same distance whether you're cycling the action one-at-a-time, or have stuck a crank handle on the side to emulate a gattling gun.)
so no, Autocannon ammo has to be functionally different depending on class, because bullets' don't pop a parachute and land gently past the point your sights are no longer effective for predicting the general outcome. (a 9mm fired at 45 degrees is lethal out quite a lot further than one fired using regular sights. Accidents can happen out to a mile away using .22 rimfire, a much milder load. when you get into 'rifle calibers' it can get absurd quickly).
Recommended Reading: "Hatcher's Notebook" (I have no idea how many printings that reference has had, my oldest copy dates to the 1960s and my newest to sometime in the 1990s, and it's still commonly referenced for firearms experimenters, handloaders, and competitors.)
A more 'rational' reasont o account for the range differences between AC 2 and AC20 might be to consider all Autocannon ammunition must fit into a specific length to feed, and that that length is decided by how big an opening you can have through the shoulder and elbow joints of a battlemech.
AC/2 can therefore have more propellant relative to the payload delivered on the other end with a better ballistic coefficient-which explains the longer range, within the same total, loaded, cartridge length (and maybe diameter) when compared to 5, 10, and 20 classes.
Hence the longer effective range for lighter autocannons-they can push a shell with more propellant, and the shell can be better shaped to pass through atmosphere (ballistic coefficient) while your 'big bores' are fiting big, blunt objects that lose energy in atmosphere more quickly and start with less of it to begin with vs. their inertia.
for real-world comparison, a 5.7x28 is going to have a longer effective range than a 9x21 or 9x19 cartridge that can pass through the same magazine opening in the frame. (or fit the same cylinder if you like revolvers)
a 'mech's arm is a complex jointed structure, there's limits to what, and how much, opening you can put into that joint before you can't feed something through it.
We actually see this with .50 Beowulf vs. .223-both fit the magazine well of an AR-pattern rifle, one has absurd energy transfer at close range and no long range performance, the other has long range performance and good accuracy.