It's the sort of thing you'd have on a Wiki page about typhoons, but I don't think it's really dictionary entry material.

That's a pretty significant commitment, Nicolas, to keep all typhoon entries continually updated. 
Remember that JMDict has been around for 30 years and might very well be around for 30 more, if not more still.
I think this is the kind of thing that's more suited to other kinds of databases, like Wikipedia.

Regarding your second point, I wouldn't mind adding the other 台風第NN号 entries and keep them updated, if there's consensus to keep this. I don't see how it's obvious, though.

https://ja.wikipedia.org/wiki/平成5年台風第13号

A few comments:
(a) it's not a "named entity" as such; it's a nomenclature system used in Japan for typhoons. A bit like "5th District Court" or "7th Congressional District".
(b) I can see it's probably useful to record it somewhere, but not here.  I can't see it really fitting into the main dictionary unless we were to put in the full range of 台風第NN号. After all, it's a bit obvious, especially its full form such as 平成5年台風第13号.

Can we just leave it pending so more editors get the chance to see this?