If you're working in another country, you're not spending money on tax, rent, food, utilities, etc. in your home country, you're spending them in the host country. Most of your income is spent in the host country. For your own example, most H1Bs want to live and spend their money in the US, not send money back home.
So it's actually a terrible 'trade' for the originating country, they lose skilled workers to the US, workers they paid to train and educate, for nothing in return.
What's the 'trade' you talk of? Labor is not trade because what does the home country get out of it?
Free trade is a completely different kettle of fish to free labor markets.