On the other hand, taking those parts of Known Space that actually made it into Star Trek and then developing them in a uniquely Trek direction offers story potential as well. And while I understand the concept of cleaning up the "extraneous" (if not really superfluous) elements in the story, I find it difficult to see the motivation, either from the viewpoint of the 1970s presentation or from that of later development of the Trek universe.
The Slavers of TAS are extremely vague, their only relevant attribute being that they are explicit bad guys (and ugly, too). This gives the automatic excuse for there being spies who would want to resist them - or, if we want to cut corners, for these bad guys having devious spying gear of their own because of course spying is naughty. Either path can be traveled further, without the need to bring up the Tnuctip or the big mental weapon that killed them all. The Kzinti can be developed without having to mind Outsiders or their eugenics programs. The stasis boxes need not have anything to do with deep radar now, but their takes-one-to-know-one attribute opens all-new possibilities. Etc. etc.
Niven wrote enjoyable Kzinti. But he also got caught in a "Protector trap" of sorts, in which the great concepts he developed put great limitations on what further ideas he could or would introduce. Doing it all Trek style would dodge the trap, essentially doubling the fun we can have with the Kzinti.