Why? Because if it's a decent and workable bike, then spending $60 on tires and tubes is no big deal if it gets you riding again. If you need a new quill stem and no shops in your area carry them, then figure out what size you need and pick one up on eBay for $15. You're still spending several hundred dollars less than it would cost to get even a passable bike.
Your analogy is flawed because those things are not remotely hard to find. Fixing your old Schwinn to use for some off-season training is not analogous to restoring an antique car.
Sheldon is rolling over in his grave right now.