LH was protecting M&M and attempting to prevent mass defections to M&B and M&S by their core members based in northern Europe when A3 & TK would not use M&M. M&M is worth a lot of money to LH. They also disincentivised travel on TK by cutting tier miles to 25% of those flown to encourage people to fly LH group if they wanted to retain status.
LH are very protective of their home market hence the relationshop with TK, LH sponsored their entry to *A but LH didn't bargain for TK utilising their access to European open skies and their far better products in both business and economy to enter the German home market. LH have successfully objected to the Gulf carriers getting the level of access TK have albeit using A320 series rather than wide bodies.
TK and A3 were meant to simply feed LH services rather than have ideas of their own but things have worked out differently. At the present time the LH/LO relationship is souring as LO develop ideas of having their own long haul services. OU are simply a feeder of LH outside of their domestic network and a few European trunk routes, the main OU service operated several times a day is ZAG-FRA. Adria are lined up in the same way.
M&M for many A3 pax would be scheme that many would never gain any status in. In reality to achieve *G in A3 for the first time it's no easier than *G in Eurobonus although requalification is easier if you fly A3 but unlike M&M there is an annual requalification requirement. I don't understand TK status but I think it's marginally easier to attain. A3 and for that matter TK prefer to look after their own loyal passengers which after all is the point of a frequent flyer scheme rather than lining the pockets of LH.