Fun toy for Kit, I would think. As though positional ICE needed any more nails in its coffin...
Anyway, if you're using this with Kit then it's guaranteed to work on the first ICE you encounter each turn. This can lead to fun situations like:
Bypassing ICE deeper in the server by swapping it with the outermost piece. This requires you to encounter the outermost piece twice...unless you're using Spooned, in which case you can choose the trigger order (as in the Prey ruling above) so that you swap the ICE you just passed deeper into the server you're running, THEN trash it. Net result: The ICE you swapped it with is now behind you and you never even had to touch it. (EDIT: Apparently this doesn't work with Spooned due to trigger timing, so you would need to in fact use Prey itself for it to work)
Find a server with a Barrier on the outside, use Surfer to go all the way in, then use Inversificator to put it back on the outside of the server ready for next time! Requires Kit/Paintbrush/Tinkering/Egret, and with the latter two you can do it multiple times in the same turn. As a bonus, you can use this to PUT that weak barrier ICE in position to start with. This is especially fun with Egret because you can just slap that on any weak ICE, put it in front of the server you want into, and go to town.
Ruin positional ICE (duh)
Stuff things you don't like on servers you don't care about so you don't have to think about them any more.
Hit R&D with an Indexing and weaken the ICE on it at the same time, making the follow-up run much easier (see also: Möbius, Medium, and the more general idea of making follow-up runs against the same server cheaper)
Swap unrezzed ICE onto the server you're hitting, then Blackmail your way past it either now or later.
Swap rezzed ICE onto a server you WANT To hit, then run it knowing there's no nasty surprises waiting for you. (In general this lets you avoid specific pieces of unrezzed ICE for the cost of running and breaking a Code Gate first)
Most of this works without Kit, of course, but it's so much more universally applicable with her and hard to justify the cost without being able to eke out some serious savings in the next few turns after installing. Probably consigned to the jank bin anyway. Still a good fun way to get into servers in style, though.
(EDIT: Comments have pointed out that Adjusted Matrix is helpful in the same way that Kit is, and that multiple copies of Inversificator allow you to use it multiple times per turn! These are both good things to keep in mind)