This card is truly balanced masterpiece with careful non-confusing wording.

While it may seem overpowered at first glance fear not, as it was carefully tested (probably by the same testing team that suggested lowering Corroder influence) before printing.

If you are thinking about building deck with this card then you should probably think again because this card does almost nothing and you have to waste clicks for it to even work! Imagine this situation: during the game you clicked this card let's say... 15 times. Now when runner breaks the Tollbooth and Archer that are protecting this card (it would cost mere 50 credits, which runner can easily get when you are busy clicking this useless piece of cardboard) he can trash it for 4 credits and 1 click! Clearly this is really ineffective usage of your clicks and you shouldn't really play this card.

When somebody complains that this card is too powerful it's probably because they are playing non-efficient breakers such as Corroder or ZU.13 Key Master or maybe they are not using the time you are giving them (when wasting your clicks on this really under-performing card) to put pressure on you by breaking your ice for 20 credits each.

To sum it up:
- very balanced,
- very clear wording that won't make any confusion,
- runner can easily trash for 4 credits or even 0 with an Imp,
- it only adds strength to rezzed ice.

Despite it's many obvious flaws maybe some kitchen table players find it fun.

kappa
One flaw in your analysis here is that you still have an action window between the Approach (where you rez the ice) and the Encounter (where the strength pump is relevant). So the adding strength only to rezzed ice isn't to big of a downside. —
To mitigate this card's uselessness, play it in an Industrial Genomics deck, with Guard on top and Caprice Nisei on Archives. The runner will surely give you big bellow laughs for wasting your time on such a complicated combo. —
My favorite thing about game nerds is when they flip out about how OP something is, and then it turns out to just be meh. —