indeed, which returns us to the constitutional question, is it a treaty or not, and if it's an executive order, does one president have the right to tie the hands of his successor?
The U.S. can’t quit the Paris climate agreement, because it never actually joined
under the US constitution, treaties must be ratified by a 2/3 supermajority in the senate. Obama claimed that it was not a treaty and therefore did not need to be ratified. No other country seems to have taken this approach: those countries which require ratification under their laws all did so, except for the US
There's a school of thought that, rather than withdraw, Trump should submit the Paris accord to the senate for ratification, where it will fail to be ratified.
But even in this view, if Obama was within his rights to treat it as a non-treaty, Trump would be entirely within his executive rights to interpret it differently — as a treaty requiring Senate consent, which has not even been sought yet.
and looking at what other countries have done,
Countries seem invariably to have accepted the agreement as a treaty that requires going through their internal treaty-ratification processes, typically submission to the legislature. Countries from the United Kingdom to China to Jamaica have ratified it through their legislatures. So has Brazil, Japan, the Philippines and Australia. In the latter, the question of whether it was a binding international accord requiring submission to Parliament received some discussion, and a parliamentary analysis concluded it was a “major treaty” that needed to be submitted.
I know of no country that has taken the U.S. approach. All countries seem to understand that ratification requires using the domestic procedure for ratifying treaties.
If you accept Obama's position that this is a "sole executive order" (SOE), then the withdrawal provision raises constitutional issues because it limits the powers of his successor. If a president can do something by executive order, then his successor should be able to undo that same something by executive order.
A extended withdrawal period in a SOE would allow one president to unilaterally pre-commit his successor and limit the latter’s powers. Moreover, the four-year period does not appear accidental, but rather, designed to limit Trump’s ability to exit: If he does not do so now, his potential successor will have the ability to cancel the withdrawal before it takes effect.