I've used Bardahl for H/A PSF after my first Honda purchase in the mid 90's. Now I use Prestone for H/A PSF, many years and lots of miles. Never an issue and all have original pumps, or had when disposed of. So the two aftermarket 'for H/A PSFs' have worked well for me and Prestone will continue to be my go to. It's readily available at WM.
Not familiar with MB CHF11, but unless a for Honda spec could be confirmed I would not use it. Same goes for using just any PSF or ATF. Wouldn't use either of those.
The only other than for Honda/Acura PSF that I find intriguing is Prestone PSF labeled for "Asian manufactured vehicles". It's advertised as a:
Premium full-synthetic formulation specifically engineered for Asian vehicles, including Honda, Acura, Toyota, Lexus and all other Asian manufactured vehicles
This formula of Asian power steering fluid is not only designed for extreme temperatures, it also provides excellent low temperature operation while protecting against wear, foaming and corrosion to maintain optimal performance and deliver excellent oxidative stability for extended fluid life.
The one negative is, at WM it's more than two times as much as the Prestone for H/A PSF. Since the latter has worked well for me, no reason to pay the extra for Prestone Asian Synthetic PSF.
So beyond Honda PSF I wouldn't use anything other than a PSF specifically labeled for H/A and from a reputable brand.