Why do radiation hardened IC packages often have long leads?

It isn't directly related to radiation hardening, it is related to the packaging. Rad-hard and other high-reliability parts often come in flat packs. The user is expected to form (bend) and trim the leads as needed for their application. Long leads allow more flexibility (options).

Taking the example of the chip in your picture (RHFAC14A - datasheet,) they aren't always in the flat package with long leads (FPC-14.) They are also available in DILC-14, which looks more like a standard DIP-14.

So, the flat, long leaded style isn't a requirement of the radiation hardening.

Wikipedia says that type of package is known as a "flatpack" and that it is a package specified for the United States military.

And, there's your explanation for why radiation hardened parts often come in flatpacks: The US military is one of the larger (if not largest) purchasers of radiation hardened parts. You get a lot of parts made to meet that standard just because the US military is one of the biggest customers for that kind of thing.

As well, they've been making the "flatpacks" since 1962. Those are surface mounted parts that have been around longer than there was any real market for surface mounted parts. Anybody who has been building small devices since before SMDs became a standard thing would have likely had to use the flatpack devices if they needed surface mount style parts.