Generally parking them will be more profitable than flying them that far.....
I'm doing plenty of money with some of them. Transatlantic lines with 120 demand & 737-700 are usually very productive. I also have some funny E190 flights from Nice to Western-central Africa(Nice-Nnamdi is an excellent money-maker, 2080NM, 90 demand) that are making quite nice money.
That being said, there are 2 big drawbacks :(1)
it loses a lot of money for the first months. So it shall NEVER be an initial strategy. It's an excellent compliment, but the investment is much more than the price of the aircraft & the slots, unlike shorter routes.(2)
it's prone to bad events. A bigger plane goes on the line, and takes all the demand. Or the demand increases, and the "too small penalty" kicks in.
And, of course, you'd better micromanage your prices. If not, you'll barely break even. With proper prices, you can really make a lot of money there. Be sure to take time to babysit your lines.
TD;LR : only for experts; and only when all other possibilities are exhausted.