The speaker voice coil is easy to test for continuity, also like a meter with a D'Arsonval movement, if you apply a low DC voltage to it it should move, in for one polarity and out for the other. If you get continuity or hear some scratchy sound but dont see some motion, or nothing happens at all, but the voice coil shows continuity and some low resistance, the speaker cone likely needs to be removed and possibly it and or the surround needs to be repaired or the coil needs to be rewound .. it likely will be a fairly straightforward process.
This is actually not that difficult if you have the supplies to do it. There are companies that specialize in speaker components and repair supplies, one is the company ("Parts Express"
https://www.parts-express.com/cat/speaker-repair-parts/23 ) (They also make and sell the great inexpensive Dayton Audio speakers).
Generally, this depends on the speaker, availability of a direct replacement, costs.
Don't assume new is always better. Many older speakers are worth repairing, especially when made with super high quality materials that are rare to see in consumer products today. If these old drivers are repaired with modern materials you may end up with a really good speaker, it may give them a totally new lease on life.