Actually, the odds of critical hits in the standard BT game would be FAR worse with 1D12 than with 2D6.

First, your odds of scoring a possible critical hit (natural "snake-eyes" roll of 2) goes from 1:36 chance (only one out of 36 possibilities) to 1:12. Then, the odds of the possible critical hit actually becoming one requires a roll of 8+ for 1 critical, 10+ for 2, and 12 for 3. Rolling the 8+ is comparable either way, but the odds of getting two or three critical effects jump up substantially, from 6:36 (1:6) odds for two hits to 3:12 (1:4), and from 1:36 for three critical effects or limb blown off up to 1:12.

That's triple the odds of a possible hit, compounded with triple the odds of blowing an arm, leg, or head off a 'Mech if you do score a critical.

Using a D12 for the rolls for hit locations would make arms the most likely targets, rather than the CT, since there are TWO possible numbers for each of them, rather than one like other locations.

I've often thought that the granularity of to-hit modifiers in BT wasn't quite enough, and that either 2D10 or 3D6 would have been better. Using 1D6 for most rolls, as in WH40K, always felt wrong, since even a +1 or -1 difference was enormous, and in many cases a +2 or -2 would be an automatic success or failure. A +4 or +5 modifier in Battletech is often still within the range of playability, so it allows for more things to affect combat, and with degrees of difference between stop, slow, fast, and "what was that?", or "in your face", close, not so close, and far.