In addition to forcing the runner to break expensive, or high strength ice and most of the points serious makes, there's a very special list of cards that gain tremendously from a 1 influence upgrade:
Grail Ice and most notibly Komainu.
OHHH BOY my favorite card to encounter, but it's better you encounter it twice in a single run. If you manage to afford to break it once, the second time is twice as expensive (and the third, if the stars align, is pretty expensive, in the order of breaking 30 cumulative net damage)
Similarly, grail ice can add multiple subs, galahad and merlin providing the most interesting stacks of subroutines, with similar self-depleting stacks of 2 net damage or program trashing (or some combination of those)
You see someone put an upgrade in Jinteki or the foundry after O&C comes out, and you'd better watch out!