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Modern corporations (at least those with cash balances that matter) have a choice of monetary systems, and will overweight those competing for their money and underweight those penalizing them.

On a multinational scale penalizing Apple and Ford cash reserves, but not extending the same penalties to Samsung, Xiaomi or Toyota, gives the foreign players greater flexibility.

It's actually higher prime interest rates. Sure, people can borrow at 3% interest (or whatever is provided) but why would banks want to necessarily want to loan out at such a low interest rate?

I don't understand the question. Are you asking why would banks use negative rates?

Pretty much. What's in it for the banks to loan out at incredibly low rates? Remember that there isn't only an aversion to high interest rates for people trying to secure loans. The banks want higher interest rates to make loaning worthwhile.

what if us-corps keep most money offshore?

Aren't most first world central banks going negative interest rates already? I guess they could always try to park cash in Venezuela.