I am sure there are,many sides to this discussion, but my own personal view is that I think some form of MOT is a good idea.
It would have to apply to all braked trailers. This would set a reasonable base line. It would only look at those featuers that affect roadworthness. (just as in cars)
The process would have to be set up like the car MOT's with certs being issued by approved and regulated test centres. It also would incorporate an appeals or complaint procedure.
Currently, you have no confirmation at any time in the life of a caravan that any part of the running gear is working effectively. Even from new some caravans are not roadworthy, but with no formal independant test you may not even realise it, until its too late.
Having to consider an annual test would help to ensure owners take trailer safety seriously, and give some confidence to the owner that they can comply with the roadworthyness laws.
As for registration, I belive it is a requirement that all braked trailers have serial number and date of manufacture inedlibly marked on the chassis, so traceability should not require new technology, just more of what we have at the moment for cars.
A test should not cost an arm and a leg, because the tes wold be far less involved than for a car, but what price safety and peace of mind?