That sounds like a good job, surfing Ebay all day. I can do that, where do I apply?
Yes, the Treasure Items would be fun to track down (but mostly they're described as from an "old" collection or not British so I doubt if you'd earn any bonuses for getting people's collars felt. Laundering by description is a piece of cake.)
And it would be a depressing job - as you'd also notice the 600 British non-treasure antiquities, often museum quality and mostly unreported, on offer perfectly legally EVERY day.