I’ll start to answer this one. In short: yes. NEH is particularly vulnerable to Security Testing, but it forces tough decisions on pretty much all corps. Having a legitimate threat to archives is much stronger than you seem to think it is–forcing the corp to spread their ice thin (especially early) is incredibly useful.
More importantly, Security Testing pairs well with other powerful cards like Datasucker, John Masanori, and, like you mentioned, Desperado. You can spend one click for 3 credits, a Datasucker token, and a card. That’s ridiculously good. With stealth Andy becoming more popular, it’s also not uncommon to simply spend a Cloak credit to net 3 ‘real’ credits, which throws a wrench into your idea that Security Testing becomes worthless when a server is iced up. Even if you were paying two credits to break the ice, you’re still getting your Desperado and your Datasucker/Masanori/etc.
All that being said, it can certainly be turned off by certain ice layouts and playstyles, but that goes for anything. Most of the time it can be the backbone of your economy for the bulk of the game and put enough early pressure on the corp to put them in a really bad position really quickly.