When you apply EQ in a digital crossover you have to make sure the signal will not exceed 0dBFS, which mean you have to either only use negative EQs or lower the overall level after applying EQ.
The worst case scenario is constant directivity compensation in a horn system, where you will typically need to raise HF levels by some 10 to 15dB depending on the driver/horn combo. That means the signal around 1 or 2kHz will need to be 10dB to 15dB lower than in the top octave, ie -10dBFS to -15dBFS.
Here is the example of the JBL M2 EQ curve:
By doing so you effectively lower the maximum level you can output but keep the residual noise (noise floor) unchanged, which means you lowered the available dynamic range.
So now let's say you have 110dB of dynamic range in your DAC. With a passive system and a properly chosen amp gain (and assuming no other source of noise in the system, especially the amp) that means that you could possibly achieve, as an example, 0dB SPL at -inf dBFS (noise floor) and 110dB SPL at 0dBFS (max peak level).
But now if you need to apply 15dB of EQ you only have 95dB left, which means you have to either raise your noise floor or lower your max SPL.
And that example assumes a perfectly matched gain on the amp (ie sensitivity = 0dBFS, and an amp with good DNR too).
This is where DACs with very high DNR come in handy.
Of course in a real world scenario in the case of constant directivity compensation things are not that bad, because your system will never have to reproduce a 0dBFS signals in the top octave thanks to the power distribution of music, so you can allow your digital EQ to go past 0dB there...