But Trump is the president.  He gets to decide how to do the deal.  I.e., he doesn't have to impose any kind of carbon taxes or give money to other countries or nothing.

He could literally just *do nothing* but stay in the deal.  AFterall, not only are their no penalties, but the only thing the deal requires you to do is set targets and publish your progress.  That's it.  And with no penalties for not meeting, why not just stay in? 

The only reason is to give a big middle finger to the international community.  That's the only reason to withdraw.