Trubel said in the last episode it makes sense they would want Grimms on their side because they want to keep their heads. In other words, better to make them friends rather than enemies who would kill them.
Renard also mentioned Nick is the very first Grimm ever to befriend/fight alongside Wesen. That would explain why they would approach Nick (though they should have considered the possibility nil once they forced Adalind to leave him with Kelly).
As for Kelly, there is also a possiblity he may be the first Grimm-Wesen hybrid ever. His potential has been speculated for a while now. Perhaps BC is aware of what he could potentially become.
I don't think that Black Claw wants Grimm's on their side. I believe it is a ploy to just use Nick so they can gain more power. Keep him to get more information, since Nick has been working with HW. I think the ultimate goal for Nick is to capture him, and then kill him after getting info from him.
Nick would be a resource, but BC has shown it's willingness to burn their assets as soon as they stop being useful.
They haven't been coy about trying to kill him or his allies. They've found him hard to kill, which the reapers, wesen council and royals all found out the hard way. Either they have to just give in and have him shot, or they try to trick or coerce him into turning over the info they want then kill him when he's at their mercy.
Bonaparte's suggestion that Renard try to recrute Nick, that they had a place for him in BC may have been a lie. He was just trying to keep Renard's conscience from betraying that it was a trap. Assuming Bonaparte knows anything about Nick's personality, he would know that was a long shot.
If Boney knows Nick's character, the whole Renard for mayor/get Adalind away from Nick and play house with Renard might all be designed to bait Nick into losing his cool. All so Boney can get at the Grimm bloodline info.
This goes back to the question of how capable are wessen at detecting other wessen? If a Wesson doesn't have enhanced senses like Blutbads or those cobra headed things that the royals used to ID Monroe early in the series, they have to wait until someone outs themselves.
Also, can wessen spot others when they partial woge or do they have to wait for a full woge like the typical human?
A Grimm's detection ability may exceed that of wessen in general and therefore a valuable asset even to a wessen-centric organization like BC.