Min is not just Rand's concubine, she can see the future, just having her there, she tends to see people's deaths, if she'd seen Rand's entourage looking are f'd up and/or dead she could warn Rand about, and while her predictions are never wrong and can't be changed, well, Rand had a lot of reason not to be in highest paranoia when Min doesn't say something like "Hey, just about everyone in your party is going to die soon by violence, just a little heads up"

Obviously Cadsuane was there as an advisor slash muscle, Nyneave and the others were there for that too, and this is basically the crew that just wiped out a hundred thousand trollocs, and not long before that beat the tar out of the FS at the Cleansing, under the circumstances including a non-combatant who can see the future doesn't really seem very stupid except in hindsight, what with about half of the known top rung of powerful channelers standing there.

Now Cadsuane, had she been thinking about, probably should have given rand the trinket, but do keep in mind that for all the crap she gives him, she is actually quite aware that Rand is capable of protecting himself from even the FS. What's more, they could easily have offered, or Rand asked, the latter is highly unlikely and had the former happened behind the scenes or not at all, Rand probably would have turned down the offer. I think, all things considered, neither Cadsuane or Nyneave would have even bothered to offer, since they'd know he'd refuse, or if it was a non-OP use terangreal, give it to Min.

Now, if either Cadsuane or Nyneave have a MAt-esque trinket, they should have stuck it on Min, esepecially since I believe both are aware of the bond, and Cadsuane certainly knows what happens, and consider how Nyneave acquired Lan, I would assume that aspect would be on her mind.

Now, moving to Rand, he picked who came along, and he literally brought an army with him, not including the one he left a way's back to reinforce him. Basically everyone with him besides Min is quite capable of protecting Min while fighting off any channeler short of a FS. I'm surprised no one else stopped the attack, but then, in the sudden shock of the situation 'guard the most powerful channler in the world' may not seem necessary.