What's the upside of this? Seems like it would only make links longer and more annoying to type in, when the intention is to make civic participation easier.

It's more compatible with the kinds of bureaucratic roadblocks you might find in a large organisation where they won't let you touch the main website, so your project has to live on a subdomain.

bingo

I’m genuinely curious: why should it be on a separately managed DNS record?

There wouldn't be any benefit to it. They're not accepting user-submitted content. I doubt anyone working for the NYC would upload CP and share a link to it.

That would make sense if it was third-party content, but its not.