Actually, there are, mostly tanks that were made under an exemption many years ago, that the manufacturer let the exemption expire when it lost interest in the scuba market or went out of business, back in the dark ol' ages before people realized that it was possible for someone other than the manufacturer to renew the exemption if the manufacturer didn't.
Probably the most common of these is the Norris E6688 aluminum exemption tanks. Norris let the exemption expire when they go out of the scuba business, and thousands of the tanks became orphans, illegal to fill or hydro. BTW, we looked into renewing the exemption but were told it had been too long since it expired. Ironically, Norris almost did the same thing again with their recent steels when they decided to leave the scuba market again! Kaiser also made some SP6576 tanks which the expemption for has long since expired. However, all these tanks were made a long time ago, and in not great quantities, so you are very unlikely to come across one. Any Luxfer or Catalina tank is legal to use and hydro, assuming it passes inspection.
There are rumored to be a few others like the Kaiser SP6020 that had the exemptions revoked because the tanks proved unsafe in service, but this is hard to confirm. A lot of shops will tell you the E6688 Norris tanks were pulled because they were unsafe, but they were not (at least, not any more than any of the other 6351 tanks) - it was just a paperwork thing.
Note that just about all these tanks were early exemption or special permit aluminum tanks, made before the DOT extablished the 3AL specification for aluminum tanks. Most of the aluminum exemption tanks, including E6498, SP6478, E7042, were grandfathered into the 3AL specification when it was established, and should have been restamped 3AL at the next hydro, however occasionally you will find one that wasn't. While these are all still legal, most of them are 6351 "bad alloy" tanks and not a good buy.