In many areas fan made mags or publications can be seen as a sign of the success of the original thing.
Far from harming the latter, they work as a living advertisement to it and stimulate innovation from the gate holder.
ASL is the wargame with the most dynamic fandom production, with some well organised TPP. I don't think many of them make a lot of profit - if they do I don't care.
VASL itself has been a major fandom creation, which has spilled out of the ASL micro universe to benefit hundreds of other wargames.
So TPP are certainly not a threat to MMP.
And even if someone sticks to the official products, they will play fan made scenarios the AH/MMP recycled in their publication loop (Tactiques, Dispatches from the Bunker, Le Franc-Tireur, Friendly Fire, etc. have fed the stream of AH/MMP Annuals, Journals and Action Packs).
As of CH, it is interesting - and quite expected - to see that the OP question is hardly addressed in this thread, but that most people explain why they DON'T buy their products.
The fact that we hardly see any of that negative view for other TPP is telling.
And when someone believes that it is mostly due to some anti-CH propaganda or lobbying, I would tend to think that it is a paranoid view of the situation from somebody who cannot or won't face the fact that there is a real problem.
Most of us have actually tried CH.
And stopped after some bad experience.
However, I would say that CH did contribute in the success of ASL at its beginnings. Perhaps a little now - just by making the game visible - but with so many extremely debatable ways of proceeding, that the negatives outweigh massively the positives.