Toasters do have a thermal fuse in them, somewhere in the element path. Might not look like a fuse but is there in some form or the other.
As to Weller, they make different transformers for 120V and 230V, different standards to conform to with each one in different countries, so much easier to conform one to EU specs ( which require primary side thermal fuse) and the other to the old US spec. Cheaper than having to recertify every single product again, with a major part change like that. you can see that in pics of them, US one no fuse, EU one has the tell tale third connection showing they have a fuse. My Weller WTCP-S, from The Cooper group 11-91, does have both primary side 0.315A slow blow fuse and thermal fuse in the transformer primary. This is the "travel iron' as it goes out to functions, even though the magnastat switches, heaters and tips themselves are getting expensive. Can buy a Solomon complete for the price of just the heater, tip and magnastat.