Because making a NATO member a Chinese puppet would be too costly
Belarus is already part of the Union State with Russia, a member of the ODKB, CIS, Customs Union, and Shanghai Cooperation Organization. It does not seem to bother China, that Belarus has divided loyalties. This tells me that it should not be a problem for China if someone is a member of NATO also. In fact, after some 10 mins of research right now, I learned that China has in fact bought the largest port in Greece (Piraeus). Recently, also, China bought a share of the largest port in Germany - despite protests from Scholz's party. So... this argument of yours does not work.
Hmmm......... you mean Putin is so easily duped by a confirmed idiot???
I think... that Putin allows this idiot to think he duped him, each time, for yet another $10-15B in exchange for promises of integration that he does not plan on following through on. The hope is that at some point we can be rid of this idiot, but that the things he agreed to will have to be honored by the Belarussians. Two years ago we had a chance to get rid of him, but he went full Rambo/Saddam, and the moment was lost.
As for Lukashenko himself, I think his plan seems to be to become president of Russia, and then later for his son to be the next president of Russia. I think this is the whole appeal of the Union State for Lukashenko - that it gives him a path towards becoming leader of Russia. I pray to God this scenario never comes true.