Is it worth repairing this spigot?
I have rarely found a faucet I can not repair. Yours needs a new valve stem packing no problem even if you cannot get the handle off. 
Move the nut as far as you can to the handle.
I use expanded goretex rope for valve stem packing, some has graphite and is easy to install. 1/2 a dozen wraps of this will solve most valve stem leaks. I replace the washer when I do this screw the valve back on then tighten the jamb nut, if it still leaks you can loosen the jamb nut and put more wraps of packing, in a pinch I haven used the Teflon tape quite a few more wraps are needed but it will seal. Tighten the jamb nut and turn the water on again. I have repaired valves that were over 100 years old doing this 5 minute repair procedure.