When I received a huge amount of cash some years ago, my outlook changed completely. The first thing to do was to split the money in order not to keep everything in one basket. I choose banks with unvieldy, problematic protection schemes that are awkward to use. And I set up a dedicated old laptop for banking (which still works).

My biggest paranoia wasn't about remote access though. I was really afraid someone could counterfeit my ID and just cash out as much as they could get away with. Fortunately, it hasn't happened to me.