Your concept is that neutral shouldn't need circuit protection, because it can't possibly flow more current than its partner hot. Oh, yes it can!
Where else would the current come from? Another hot. It's quite common for two hots to share a neutral.
Properly done, this is called a multi-wire branch circuit (MWBC); and in this case the two hots are on opposite poles, with neutral handling only differential current. Ergo it's mechanically impossible to overload neutral. Try all the combinations!
Happens all the time that people move MWBCs around and put both hots on the same pole. Now the neutral returns all the current for both hots - and you're gonna want that fuse.
It was also common, especially in the K&T world, for installers to play fast-and-loose with neutral: first running hot to a point-of-use, then running neutral back to the nearest convenient neutral, who cares. This isn't even an attempt to MWBC. Here, too, you'll want that fuse.
Blowing (only) a neutral fuse is not that big a deal - yes, it will light up the neutral wires at line voltage, but neutral is supposed to be insulated for that. It's bad news on an MWBC, as now the loads on each pole are in series, and one will see greater than 120V while the other sees less.
Nonetheless, because of the mischief that can happen on MWBCs, there's now a requirement that neutrals have common trip with their partner hot(s).
Do not up-fuse the neutral. If you feel obliged to do something, down-fuse the hots. However you should know that you cannot rely on overcurrent device sequencing (i.e. expecting the smaller breaker to trip first). Ask anyone who's put a 60A breaker on the #6 feed to their shed, and a 40A main breaker in the shed subpanel.
If you have not carefully mapped all the circuits, you could do some testing in the fuse box to identify and fix any promiscuous neutrals. Absent such testing and mapping, I would not simply eliminate neutral protection because it doesn't feel modern enough. I would fit a 3-phase panel and treat neutral like a phase, using 2-pole (3-pole for MWBCs) breakers on hot and neutral.