The strategy of using your local ID (and hiding your U.S. status) will work for a little while longer. Google for the acronym "FATCA". Sooner or later your bank will ask you to certify that you have no U.S. connections.
No, the real key to keeping your paperwork simple is to keep the balance in all of your non-U.S. bank accounts below USD 10,000 at all times. The form is TD F 90-22.1.
Your U.S. tax return should be vastly more complicated than a resident's return if you want to avoid double taxation of your income. You will either be attaching Form 2555 (to exclude income from U.S. taxation) or Form 1116 (to claim credit for the taxes you pay in Poland) or both.
If you have a little investment account with some savings in it and you buy mutual funds, you will be filing Form 8621 for each mutual fund you buy.
If you are a startup entrepreneur and you own stock in your company, you will be filing Form 5471.
Seriously, it's a pain factory. I'm glad you have found a simple way of doing things, but for most people the annual cost of doing this paperwork is staggering.
