I haven’t tried using my setup to embed frame wire into wax (I use plastic PF120 frames), but from what I’ve seen on Youtube and this forum, it sounds like many people do use power supplies or car batteries for that purpose.
My foam cutter uses a special kind of wire, called Nickel Chromium wire (NiCr), as opposed to ordinary frame embedding wire. The frame wire is probably made from iron. NiCr wire has a higher resistance and is used for heating elements like in your toaster, stove, or oven. Due to its relatively high resistive, it heats up very quickly when you force a bunch of current thru it. (Heat output = Current * Resistance squared). I seem to recall reading that NiCr wire maintains a good deal of mechanical strength up to 1600F whereas other metals don’t.
My guess is you could embed iron based frame wire using an old computer power supply (or a new one, you can buy new for about $20). To heat up iron based frame wire, it will probably require more current than my setup uses since the resistance of iron is less than NiCr. However most computer supplies output well over 20amps, so that shouldn’t be a problem.
Computer power supplies have 3.3volt outputs, 5volt outputs, and 12volt outputs. I’m not sure which would work best for embedding frame wire, but 1 of the 3 would probably work