Most who’d implement a high-pass filter over the main speakers would do so over an existing, passively configured speaker setup (i.e.: with a build-in crossover "seen" by the amp on its output side), meaning an extra layer of signal processing/filter of some kind is added to cut off the main speakers below a given frequency in the bass area.
If a DSP is suggested for this purpose it runs contrary to the desire of quite a few audiophiles to avoid added (or any) conversion steps in the signal chain (not least A/D conversion with an analogue input only, which would then be followed by the necessary D/A conversion step for the signal sent to the analogue input on the amp - unless it’s a digital variety), and so an analogue HP-filter may be preferred here. Purists on the other hand would rather avoid any kind of added HP-filter.
Previously I used my current DSP/digital crossover (Xilica) over my passively configured main speakers to cut them off below some 80Hz to be augmented with a pair of subs below, and being it’s a high quality DSP (even with A/D to D/A conversion steps) the result was great; I could detect no lack of transparency, resolution, change in tonality or other with the inclusion of the DSP, and being able to experiment with and find the sonically most desirable cut-off frequency to the subs (with both low and high-pass filtration) proved very worthwhile, also in relieving both my previous all-horn speakers and Class-A amplifier in the bass area.
Which is to say: with a high quality and transparent DSP/HP filtration device any remaining slight influence the filter may introduce by its mere existence in the chain as an added element (and thus, strictly speaking, can’t be claimed to be fully transparent in an isolated sense) is likely to be alleviated by the positive outcome it creates with relieving bass to amp and speakers, in addition to providing for the opportunity to tweak more effectively with the crossover range to the subs.
If on the other hand you’d run a fully active speaker setup, which I know you aren’t, the digital crossover/DSP or electronic XO(i.e.: non-DSP) would act as the only filtration means in the chain (remember: the passive XO is a filtration/equalizing device as well, and a sonically detrimental one at that) that could also apply a high-pass filter over the main speakers. This way the crossover you’re already using as a wholly necessary component (just like the passive XO) can simply be asked to perform another task, and that way you’re more effectively approaching your speaker setup + subs as a single speaker system per channel - they’re merely divided into separate boxes. This also means that the separate amps to each driver section work independently of each other; whatever goes on in each of these amps and corresponding driver sections won’t affect the other, which is a further bonus - and hardly an insignificant one.
It seems that many who attempts a high-pass solution over their passively configured main speakers for the use with subs don’t approach it all-out enough, be that both with regard to the added filter component used as well as and perhaps not least where the implementation goes; sometimes such a project is indeed doomed to begin with. Therefore, give it a good shot before coming to a conclusion.