> Is it economically worthwhile to attempt to repair them?

In a developed economy, maybe barely. Depends on the monitor, and what's wrong with it. If you're good enough at soldering, and it's just a capacitor in the power supply issue, and the case isn't going to fall apart when you open it, sure. But if you have to hire help, or replace a module, probably not.

In places where skilled labor isn't going to billed at $100/hr or more, then there's more you can do ... I don't think it's worth replacing a panel if the panel (or its wiring) go, but you can replacing modules likely makes sense, if you can source them; maybe some light module repair too if it's just cold solder joints need rewetting.