Mod version 1.0
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The "problem" with those doors was that Bethesda set the doors' state of the Eat'OTronic dispensers of being "Destroyed" once they were opened.
Once the doors were set to "Destroyed" you cannot activate them again.
Probably they wanted to block them in "Opened" state to simulate somewhat the broken state of the springs (or mechanisms) that set those doors in motion or - to put it into another light - to simply disregard such small things when they had to close the project. Yet another possible reason of why they didn't even use the closing animation on dispensers' doors (shutters or whatever).
Eat'OTronics are very rusty after 200 years; the springs or mechanisms which set the doors in motion are rusted too, even broken.
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This "fix" unset the state "Destroyed" to "Non-destroyed" when loading your last save. It does not use the closing animation.
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To be honest, the game runs OK (or something close to) with or without this "fix".
Not at all a bug that needs to be fixed - it's more on the aesthetic side of the things.

PS: If you want to test it, you find one dispenser in Tenpenny Tower 2nd floor.

Inspired by:
Callisto.

Many thanks to:
Nexus - for allowing us converting all sort of ideas into mods. And not only.