No Governor should have that power. Definitely not something that should be possible on a whim without some sort of process.
Did you even read the comment? There is a BILL, which is created by the legislature that does indeed have the power. They can both delegate their power or take it away at any time. Does that qualify as a 'process' in your jargon?
If they wish to delegate, they certainly can as the way this country works the state is the final authority in all things absent a few that the states collectively have delegated to the federal government or cities within the state jurisdiction.
I am suspicious that you have nonsensical notion of an arbitrary Executive head of Texas who can rule at whim, and am really projecting at another at a federal level mentioned frequently in these threads.