Anyone who is going to mix exactly 0.001 BTC every time in order not to pay mixer fee is obviously poor and deserves the free mix.
Well, in some scenario you could call someone like that as poor, but I guess that person might be opportunistic as he/she could literally mix his/her coins without paying any fees. Such people might do multiple mixes of 0.001 BTC in order to avoid paying any fees.
Sorry but I might have to disagree with you here, no rich person will have to waste their time and money doing multiple mixes just to avoid paying a small mixing fee, because in the end, the user is only cheating him or herself since he or she will have to spend more money on blockchain transaction fees than he or she would have spent on the mixing service to have his or her bitcoins all mixed at once.
And let me mention that I might not to too sure of the origin of this discussion since it's been like a week or more since I came online last, and just resuming today.
I've tried reading all previous discussions but i somehow missed the origin of this one, but based on how and what I understand, it is unlikely that a truly rich person will carry out such a tiny bitcoin mixing transactions as a way to avoid paying a mixing fee, very unlikely.