As for accidentally starting the mission unequipped:
I have rarely accidentally hit 'ESC' or clicked 'OK' (if you use mouse in that direction of the screen, e.g. to move back and forth between soldiers; this is a newbie problem, advanced players usually use keyboard hotkeys directly), leading to completely or mostly unequipped (or auto-equipped, if that option is enabled) teams. I suppose there could be a use case for going back to the equip screen, but that would likely also break the balance somewhat. So I don't really advocate that. I have taken my medicine as a result of me being sloppy.
As for the need to re-equip the team afterwards:
In many mods and lesser degree vanilla you don't necessarily know in advance of the mission which equipment is the best for the enemy units before you know what they are. And your strategy of whether you try to capture the enemies alive or kill them might also change based on the information you get once the mission starts. (A concrete example in XCF: out of a couple of dozen identical "environmental alert missions", you will want to catch the shadowbats and rats alive, essentially all other animals you want to kill after obtaining some samples.) So you definitely would love to see a way to change the equipment quickly.
But not knowing what to expect is also one excitement of the game and you could argue that you could break the game balance if you could just go back to equip screen and do everything from scratch easily.
As it is, I usually try to equip the team with the equipment which is most likely the best or most reliable for the situation, or in some cases duplicates. For example in some XCF missions I equip the teams to wield two guns that fit different purposes, and have everyone drop the second one once I learn of what the enemies are and thus what my tactic for the mission will be.
If XCOM was written from scratch:
If XCOM was written from scratch the game certainly could have the option the OP describes, i.e. that you can redo the equipping screen easily, possibly with some restrictions (e.g. you can no longer re-equip with the stuff carried by someone else). But because OXC/OXCE is mainly concerned with keeping the feel of the original, I'd certainly understand if this kind of engine redesign would be deemed out of scope.