Alcohol stoves can be very fast. I've done a bunch of hikes using one of those double-walled cat can stoves, and it works great. Really pumps out the heat. Very reliable, and almost as fast as my canister stove.
I have a Toaks burner, I agree it's quite fast (after the alcohol is heated enough and starts to vaporize, which can take some time when temp < 10-15 degC) but it's nowhere as fast as my gas burner.
But it's a compromise, they all have their pros and cons.
But it's a compromise, they all have their pros and cons.