The motor or drive system is designed for low voltage DC, eg. 18V or whatever, and operating from high-current capable lithium cells.
The tools could theoretically work through a suitable AC to DC power supply, but it would need one with the DC output rated within the battery voltage and able to supply anything from 30A to possibly 100A, depending on the tool type and ratings.
Plus connecting cables from that to the tool with high enough current ratings to not cause an excess voltage drop at full load current.
A suitable power supply with cables and connectors etc. is likely to be more expensive than just buying the AC version of the tool! The much higher voltage supply from AC power means the currents are proportionally lower with tools designed for direct AC connection.
Suitable batteries can easily supply very high current peaks for short periods as needed with such tools.
AC power supplies will shut down almost instantly with a current overload, so must be rated for the highest current the tool can use, even it if it only takes that for a fraction of a second at a time.
(Or you need a massive capacitor bank to smooth out the peaks, and a slightly less massive PSU).