"Does it work?"
The conventional wisdom among many transistor radio collectors over the years has solidified into the notion that a large part of a radio's collectability stems from whether or not the radio "works". To me, this seems like a red herring, distracting from more important aspects of a transistor radio's value, both as a historical object and as a collectible.
Enjoying a vintage transistor radio as a working object is a lot different than gauging its collectability by whether or not it works. One of my favorite Medium Wave DX experiences was tuning my trusty Zenith Royal 500D across the medium wave band shortly after I had arrived in central Europe and hearing broadcasters from all over the continent coming in loud and clear -- listening to these was better than any rare MW station I picked up later on with a "real" receiver, a Kenwood TS-940S with an outdoor ariel.
When I started collecting transistor radios in the 1980s, I'd guess that 90% of the American and Japanese radios I found were still working, and at that time American collectors seem fairly evenly divided in opinion over whether or not it mattered if a radio "worked". Collectors in Europe, on the other hand, were almost unanimous in their opinion that a transistor radio should work in order to be considered collectible, I think mostly because they were focusing on quality multi-band portable radios rather than inexpensive pocket radios.
So of course what happened between the 1980s and now is that the electrolytics finally dried up, and because of that many collectors are now recapping their sets to make them work again. And maybe also a circuit wire or a battery lead had broken. I have no problem at all with collectors wanting to fix broken wires or replacing electrolytic capacitors in order to get their radios working again.
I do think though that if you're recapping an early and historical transistor radio, you should save the original capacitor by taping it to the inside of the radio's cabinet - and the same goes for any other component replacements.
(One example here is my Philips Germany L1D90T "Fanette": As I wrote on its web page, "A previous owner of this unit chose to recap it in order to get it playing again -- and then he did something I wish every collector would do when they recap a radio: he saved the original capacitor -- it came to me in a plastic pouch along with some other original parts, and I've put that pouch right inside the radio for safe keeping for whoever inherits this radio in the future".)
My own personal requirement for early or historical transistor radios is that the radio's circuitry remains original, or at least that any replaced original components are kept with the radio's cabinet.
I really can't see how whether or not a transistor radio "works" is all that much important to its collectability. It doesn't take much effort to get one working again, and what do you have then? Are you going to take it to the beach? More likely, you'll take out the battery and put the radio up on a display shelf and never listen to it again.
If we're talking about a Bang & Olufson Beolit or a Royal 500H or a Zenith Transoceanic, then of course we'd want that radio to work as well as possible -- but most US and Japanese pocket transistor radios are just little AM radios with crappy audio and all sharing pretty much the same basic circuit.
My own feeling is that the things that make a radio collectible are historical significance, commercial significance, cabinet design, and circuit innovations. If the radio "works", that's a welcomed bonus for most pocket radios, and of course it's important and necessary for radios with more complex circuitry and audio value, especially multi-band transistor radios.