Yes, you are missing something here:

With most wheels where the spokes are tensioned correctly, it would be very difficult, if not impossible, to true the wheel before you started stripping out the slots with the screwdriver, especially because...

...on most wheel builds, there's a good chance at least some of the spokes, if not all, will be protruding through the nipple, into the screwdriver slot to the point that either the screwdriver will have no purchase, or will strip out the slot even easier.

A spoke wrench is pretty much necessary to true a wheel. Unless you want to try mangling your nipples with an adjustable wrench or vice grips.