I bought my boat from a local dealer in Wolfeboro (I'm in RI) and the trailer had no Ser. Number..OR ANY Trace..NO shadows of a Sticker on the galvanized trailer. The boat and trailer were about 10 years old at the time.
Lotta mail (Paper) between me and the dealer. The dealer
Made Up a Long number for the trailer....Put it in writing..It worked. OLD trailers in RI don't need "Inspection". So I guess it all DEPENDS.

NB