I just can't see any benefits to a helmet in a trailer to offset the disadvantages (99+% of my trailer use is on the road).
Aaah... a classic "YMMV" situation then, as 99+% of my trailer use is off-road (and on the road usually means a busy rural A-road with impatient holiday traffic on it who don't like bikes slowing them down on the way to their pub lunch).
What's most important is that they are comfy and enjoy it (with a reasonable degree of safety). He certainly gets pulled on the road without a helmet on (inc touring in Belgium), it's just that the usual roads we go on just make me wish he was wearing one. And yes - trailer destroying impacts weren't really what I was thinking of, but any car impact, even quite "gentle", is likely to impart a lot more energry to the trailer that virtually any "not involving a large moving lump of metal" accident off-road.
Also I'm having to tell him to take his helmet off in the trailer as he'll be more comfy, rather than having to get him to put it on. And the helmet's usually coming along anyway as his bike is often strapped to the back of the trailer!