The trailer tyres might not drive, BUT they do help stop.
When going down a slippery mud slope, you want all the grip you can find if you don't want the trailer to overtake you.
Only downside to MT's from my point of view:
Higher purchase cost..... Not enough to worry about
Noise.... Who cares on the trailer. I run them on the car anyway.
Higher fuel consumtion... In my experience makes no difference
Less grip in the wet on bitumen... Has never worried me. I would be more worried about the 4wd, but that has never worried me either, just drive to the conditions.
While I agree about the grip.. Have a think about it. Steep muddy slope, going down hill, tyres started to cake with sticky mud and turning into slicks, how do you clear the mud??
Doesn't matter what tyre you have on drive or or not, if your doing 5km an hour down a slippery slop with stick mud, your tyres will cake and turn into slicks, like a giant snowball.
Your right though, there is no disadvantage to using muddies apart from what you said, but their is no advantage either IMHO.