A lot of Big rig trucks running 24V are already doing this (tapping for 12V power). All you need is a "battery equalizer" to evenly pull a charge from each 12V battery and keep them balanced ("equalized").
Here's a great article on how to do just that!
Guide to Successful Dual-volt systems
On the flip side side... Some light duty trucks/tractors with a 24V starting system only use 24V for the starter, and they basically use the center tap method to get 12V to run everything else.
They run a 12V alternator to charge both batteries by using a charging isolator to charge 12V batteries in series rather than charging both batteries at 24V wired in parallel.
Essentially running 24V only at startup, and 12V the rest of the time. Running a dual 24V/12V system this way favors 12V power with only intermittent 24V draw.
If you have a heavy continuous 24V draw on a regular basis, You'll want both batteries to be equal (equalizer) to ensure consistent balanced power for both your 12V/24V devices.