Sure, it might take 2kW peak and 500W average to achieve the same you get from a battery with 500W peak and 50W average, but it's insignificant in energy bill if you use it for a few minutes a year.
Many if not most battery powered tools still use brushed motors. And they are not that much worse than BLDC variants of the same tool. Saying that if powered from AC, the same tool suddenly becomes 4-10x less efficient is nonsensical.
It's not nonsensical. AC universal motors in power tools are designed to high winding resistance to artificially low efficiency, which serves two purposes, (1) inrush/stall current limitation in absence of any current sensing control circuitry (so that a cheap triac circuit won't blow up on switch overcurrent; or house fuses won't blow up), and (2) cost, weight reduction due to copper savings.
Remember, in non-current-controlled DC motor, the ratio between stall current and nominal operating current is proportional to efficiency. If you make an efficient motor, stall current is massively huge and you need to actively control it, which costs easily more than $1 in parts. Inefficient motor can be directly connected to a voltage source, or PWM'd without current sense.
Battery powered tools have incentive to use higher efficiency motors because otherwise the runtime would suffer so much (and cells would need to be rated to even higher discharge). Therefore they also have some kind of MOSFET-based switch which does some rudimentary Rds_on current sensing and limitation. So yeah, they are not more expensive only because they come with a battery and a charger (with isolated transformer), but also because the motor itself is more expensive.
As you point out, brushed vs. brushless is actually quite irrelevant, you can design efficient or inefficient motors both ways. Brushless enables a bit better power density by saving the volume occupied by the brushes (especially higher efficiency brushes would be larger). But there sure are brushed DC motors over 90% efficient, used in old forklifts, early EVs, industrial applications etc.
Look at the difference in vacuum cleaners producing roughly the same amount of flow and static pressure: from 1000W of 1980's/early 1990's, up to 2000W during the power bloat season starting late 1990's, finally back to even below 1000W after EU made that illegal.
If you don't believe me, observe it yourself: look how easily an electric drill rated to 500W or more stalls and compare it to even a cheap battery powered drill. The difference in power consumption isn't 10x I admit that but 4x difference is well possible. If one is 60% efficient then the other can be 15-20%. You can also see how much more air flow the cooling fans on these cheap-ass corded tools produce compared to battery variants.
Upper limit for motor efficiency is obviously 100%, but remember that lower limit is as low as 0%, and as long as you can get any cost savings operating at low tens of %, and it's not illegal to do so, it's not
nonsensical at all. With easy availability of 1.5kW - 3 kW from a wall plug, there is little incentive to be efficient, but running with a battery totally changes the game.