I think the only actual concern with the above is that things like STAB aren't proper BP modifiers in the damage formula, which is a moot point since the negative consequences seem to be with relative damage calculations anyway. My understanding is that these relative base powers instead help newer players learn which moves are stronger more quickly. Let's look at the first part of your example:
Suppose we have a pure Water-type Adaptability Pokemon with Liquidation and Icicle Crash. Icicle Crash does 30% the first time. Let's look at what happens with and without showing relative base power:
With: You see an 85 BP Icicle Crash and an 170 BP Liquidation. I have no idea why it'd be showing 113.05; even if it was buggy and only accounting for normal STAB or normal Mystic Water, that would come out to 127.5 BP or 102 BP, respectively. In any case, assuming the display is correct, that's a comparison between 85 and 170, which seems very reasonably to indicate Liquidation is twice as strong and would do approximately 60%. Moreover, if I am a newer player who doesn't know what Adaptability does, I don't need to know! Instead I can compare the two moves and see Liquidation is stronger.
Without: You see an 85 BP Icicle Crash and an 85 BP Liquidation. To the uninformed who doesn't know what Adaptability does, he thinks these two moves are equal in power (though in this case he might know about STAB, but that's neither here nor there). However, there's no ambiguity and the move's raw base powers are displayed untouched.
Now, let's add Mystic Water to our calculations.
With: You see an 85 BP Icicle Crash and a 204 BP Liquidation. To compare the relative power difference between these moves, you could divide 204 by 85, see that it's 2.4 times as strong, then multiply that to our 30% from earlier to conclude Liquidation will do roughly 72%.
Without: You see an 85 BP Icicle Crash and an 85 BP Liquidation. You have to know Adaptability is a 2x boost and Mystic Water is a 1.2x boost. So you do 30%*2*1.2 to get 72%. Note that in this particular example, this only works because Icicle Crash and Liquidation have the same base power. If they didn't, you'd have to still do a division at the start of the calculation. For example, if our move was Ice Punch rather than Icicle Crash, we'd have to do 85/75, then multiply that times 30% then 2 then 1.2. Either way, it still requires mental math or some physical calculations to do.
So I think mental calculations are not significantly hindered by these sorts of relative base power displays, and instead it is a great boon to newer players unfamiliar with certain items/abilities/etc. Now, if this display is bugged (like if Adaptability Liquidation on a Water type is actually displaying 113.05 BP), then that's a bug that should be fixed, not a feature that should be removed.