The obvious uses are:

  • Archangel on the outside of a server, to force the corp to break or beat the trace, otherwise you bounce their breaker for the inside ICE. It's quite taxing to break, except with D4v1d. The trace is quite strong, so everyone who isn't running a Security Nexus build will probably pay 4-6. And for only 4 to rez!
  • Bounce other cards the runner needs during or just after a run. Self-modifying Code, Plascrete Carapace or Clone Chip perhaps.
  • Messing up runner cards with counters (virus/power/credits) like Kati Jones or Medium. That taxes the runner a mixture of and .
  • Bouncing expensive cards. Good targets include Femme Fatale, Professional Contacts, Yog.0 and Magnum Opus. Most runners don't play too many expensive though. Security Nexus would be a juicy target, but, well...

The trick I've missed so far is to just hold an Archangel in hand. If you can afford to trigger it multiple times, it can be a major annoyance for the runner. This is especially useful if HQ isn't very secure, inviting friendly runners for multiple visits. As an Ambush it is very difficult to trash. Typically an Imp or similar would be required. Using Archangel like this is relatively costly, but can generate a differential.

I can't believe how cheap Archangel is to rez.

I'll echo your last line. 99% of ice costs one more to rez than it does to break with Corroder/Gordian/Garrote. That's just kind of the rule. Ice that is better than that typically doesn't stop the run, or can be clicked through, or something. Archangel costs 4 to rez, and 5 to break with Garrote. That's insane. You can see what's going on. Its basically costed as positional ice. You can see similar cost efficiencies on other code gates that don't do anything on their own. Chum/Wendigo, etc. Archangel is better though, because of its permanent impact on the runner's board state. Every time someone Power Tap rabbit hole Nexuses through one of these an angel gets its wings. —
Archangel is Code Gate and Garrote is Killer. —
But it still costs 5 to break with Gordian Blade as well for those counting. —
This card absolutely wrecks OCA builds, since Fall Guy won't save a resource from being added to their grip and it won't save anything hosted on OCA because their host is no longer available. Any OCA build needs to respect any NBN deck on 3-4 credits if you aren't also filthy rich. —
I agree with Waltzard. This card is just too powerful for its cost. 5 to break with Gordian Blade! It pays for itself in one encounter. You got to be careful early game as they may run through it with nothing installed, but that'll last exactly one turn. Just put an Ice Wall in front of it and problem solved. There are only 3 economical ways past it, D4vid, Femme, and Study Guide. D4vid of course has only 3 uses. Even if the runner Femmes it, it's no big lose for the corp, they only spent 4 to rez it and it'll quickly pay for itself. Study Guide is great, breaking it for 1, but that's only after spending 3 to install it and 12 to get it up to strength. Even Refractor needs 2 stealth credits and credit. Then too the ice has the ambush option. I don't think it'll often be used, but its an option and a really good one in certain circumstances. Anyway, I don't like this card! —