The more sets I restore, the more I am firmly in the "replace 'em all" camp for electrolytics, paper and Black Beauties. Yes, you may get a set to work with a mix of old and new caps . . . for a while. After you have hauled some of those sets back onto the workbench for a second or third time, the lesson starts to sink in.
In my case, the big "defining moment" was when I burned up an expensive and hard to find power transformer, by trying it on the workbench one time too many with the old electrolytics in place.
Some people claim they can "reform" electrolytics to make them like new. I have tried that a few times, with poor results. If you would like to play a half-restored TV with ticking time bombs waiting to blow inside . . . it's your TV. I would rather be able to turn it on without crossing my fingers and watching for smoke.
Older orange-drop types (I have also seen maroon ones) seem to be a lot more reliable. Same with mica caps, although some of the 60-year old micas are starting to show their age. I had to replace a few micas in my RCA 630TS. For these, I replace only if I have a specific reason to think that one is bad.
From what I have read, moisture is what dooms old paper & Black Beauty type caps. Water vapor eventually gets through the wax or plastic coating, and the paper does the rest. This is true whether the cap looks like new, or melty or cracked. I have tested a lot of beautiful-looking paper & plastic caps after removal, and they were 99% garbage.
Modern caps have much better coatings, and they don't use paper inside -- for obvious reasons!
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html