That's not practical.
I sync my music folder with my PC, so not all my music is going to be managed in iTunes on my Macbook. If iTunes is incapable of handling external changes made to the music folder, then it really is useless to me.
iTunes does not operate in that any changes made to the "iTunes" folder will be reflected in your iTunes library. Your iTunes library will only be modified if you go through iTunes first, via "Add to Library".
This is what iCloud is for. Assuming most or all of your content is purchased from iTunes, this solution will work well. If you have a good deal of ripped or otherwise nonpurchased content, then you should use iTunes Match or Home Sharing, neither of which I have experimented with much. You'll have to ask someone else for help with those.
Also, how would I even identify the missing entries in the first place? iTunes doesn't exactly make it easy to group all those files together for easy removal.
True. No quick way to delete all the problem files to my knowledge. I remember I encountered that problem once and I had to go through my entire library by hand and delete the "file missing" items. That was a while ago, and there may be a better solution now, but again, none fo my knowlege.
Does no one use more than 1 computer these days?
Of course we do. But the concept of keeping two iTunes libraries in sync by means of the iTunes directory is something that Apple either hasn't paid much attention to, or believes is an inferior solution to iCloud or Home Sharing for one reason or another. To be honest, linking two iTunes libraries up to the same iTunes directory in order to keep them in sync seems like something Apple would never encourage.