Even if it's 99% efficient(which would be incredible), if you're recharging 100kWh of capacity in a minute, that's using 6MW. So your 1% of inefficiency is still 60kW of heat that you need to do something with. And 60kW of heat is a crazy amount.

Right, but that's the thing about efficiency, it's relative.

Another poster made some napkin calculations, even with a 99% effective process, meaning 1% energy lost to the environment, he calculated several kW of heat you need get out of your system.

Even if you have 99% efficiency, which in reality is mostly unachievable, that's still a huge loss of energy if the energy you're handling is high enough.