At first glance this seems okay. Good rez to trash, annoying effect, fair influence. You dream of all the mean ice you can put in front of this and grin.
Then you start to notice the downsides. The runner gets to choose the trash. Any recursion makes it a minor annoyance rather than a game changer if it fires. The first jack-out window is after the first piece of ice, making this useless until the server is double iced. And how often do you jack out, anyway?
If you're playing against a Jinteki: Replicating Perfection, the answer is every turn you make a run. Suddenly the double ice requirement looks easy, and a minor annoyance is just fine if they have to run it over and over and over. And the runner that goes through all of your mean ice is going to have to spend 5 to trash it, which is good by itself, but when you consider that they likely couldn't also run a remote on the turn they did that, it just becomes absurd.
So, in RP they have a choice of A) having mean things happen to them, B) paying lots of money to avoid having mean things happen to them, or C) trashing an installed program while taking one ice's worth of A or B. The best part is that in order to have the privilege of spending 5 to trash something that cost you 2, they also have to do A or B.
Suddenly this is sounding broken. All that wonderful stuff for a mere 2 credits? Here's the rub: it's not 2 credits. It's 6. Because you need one one every central. And you need them double iced. That's nine cards. Yes, you can still put mean ice in front of your centrals without it, and you should, but without three of these rezzed on centrals the runner still only has to deal with a single piece of ice to do a remote run. Suddenly 5 to trash isn't looking like such a bad deal.
Now RP games tend to run long anyway, so it's not unreasonable to think you will manage to get three of these out fairly often, but that's three card slots you're dedicating to something that is essentially useless unless all of them are out. I say essentially useless because even with two out the runner will just hit the third central's first ice if they want to hit a remote, and probably weren't going to jack out anyway if they were running one of the servers with it.
You despair! All this fun stuff is just too fragile. But wait, you think. Recursion! Of course! Jackson Howard, Interns, and can get it back for free; Crick and Architect are ice that can install it from a subroutine. Susanoo-No-Mikoto is effectively a replacement for one (or even 2) of these as well, though extremely conditional.
In short, it's interesting. Which should be obvious given I just wrote seven paragraphs about a card with one ability.