I stand by what I said seven years ago: insta-win should be gated behind 4+ tags. This makes much more interesting room for effects that work with 1–3 tags. And I think we’ve got a lot of the way there, with more cards which remove tags as part of their cost (how does that work, in lore?), as well as designs like Freedom of Information and Predictive Planogram.
I find it instructive to compare HHN to another controversial card which warped how you played: Account Siphon. I think Siphon was good for the game, but possibly a bad core set card: for a very long time, the only credible tag punishment was double-Scorch, and that could be guarded against by yet more Siphons (and Vamp). But people learned never to leave an open HQ vs Crim, and/or to have a way to sink a bunch of credits to defang a Siphon run. HHN’s counterplay is much less exciting: it says “don’t run, make money instead”. That steers runners away from the fundamental interaction in this game.
A burst of tags is an important thing to be able to deliver, especially if you want to gate game-winning effects behind high tag counts. HHN’s terminal condition was good because it meant the runner had at least one full turn to deal, but I would give tags based on the number of stolen agendas or the runner’s number of agenda points. Probably the latter, to prevent Sportsmetal/Psychographics silliness.