This is a clear cut case of interesting simply because it calls out from our brain (while playing it in a 1v1 ladder game) and shines a new light unto some previous notions we have had / experienced:
in this case, the single player campaign indoor type of map gameplay where you "empty the map", room by room and get that "breather" when you can't open a specific door automatically (usually a save point with a transmission / video / display of score or new objectives/etc, a breather that allows you to get out of the immersion you were in (for a break or for a second, if the map is hard then to save and be "reassured" from it etc))
In this map .. when you open a door.. who knows what will happen and how this will add to the 1v1 tension
= that's fascinating at the most, to interesting in the least.
Furthermore, this is nothing more than a destructible rock, what i mean by that is that people don't spend all their games thinking "more" about destructible rocks then they do about the rest of the gameplayt/units/abilities/terrain/lighting/etc, it is a part of the gameplay but does not pollute it in any way).
Sorry if my comment seemed to draw out the sheer number of doors, it was meant to

i'm convinced that a map filled with such doors (going more into the "urban / installation / INDOORS " feel) is bound to be great, but it would be THE "door to door" map

That said, i think having 4/6 such neutral units in many 1v1 maps could really be nice!
In any case i love the idea realized and that with these units like the destructible rocks units, you can allow for same or even lower base mains to work / be fun to play in a 1v1 map.
i think the mechanic is good:
that you need an attacking unit to activate it (open/close) if you want to have "many" doors in a map (i would say different if you only had 2 in a 1v1 map for instance, in this case you have "many" doors and this is defining the layout, if you only had two doors/gates, it could be cool to delegate the access (the ability to open/close it) to a unit like the worker (like the collecting of terrazine in solo campaign) or a tier 2/3 unit, so that this would define extra timings and extra gameplay (having one worker allow the opening of a back door in front of the impending invading army is great added gameplay)
i think your priorities are semi good:
3 armor and 2000 hp dps required to go from closed to open = yes
but 1200 as cost to close it up again?
opening it is a clear cut yes, you need to destroy the door
(whatever the hp the layout calls for, or it could even be different in different places on the map if this hp / armor differential is showcased graphically on the doors)
..but i really think the closing of the door should not require dps, it should be more like a xelnaga tower trigger:
"Player"x" has a unit [any ground unit] for "y" seconds on region "z" [besides the door] and then the door can be shut in real time WHEN the Player "x" decides to select it and activate/close it through its menu
If the unit leaves more than 3 seconds away from the region, you lose the ability [call it "hacking"]
if your unit is killed you lose the door's control/access to the ability in its menu
If i must be frank i think that with so many doors, it could be interesting to even do the opening of the door the same:
you need a "dedicated" worker/specific ground unit to stay alive in region "z" to open the invulnerable door (a worker seems the best but if you want to go tier 2/3:
ghost or ghost with an upgrade = opens/closes the door in "t" seconds
infestor = opens/closes the door in "t" seconds.
High templar = opens/closes the door in "t" seconds.
This would really only add an extra capture the flag type of concept that we know from many places (from fps games to sc2 team games or other morrow area control mod

.. to a 1v1 setting.
Real fun because if dps required to circulate on the map, an "x" 50 food type army squad can open, pass and then close the door in one go (with good micro skills) .. that really allows for these doors to make all the map evolve through out the early to late game, in a large palette of potential games...
The early game being all about getting to that "x" 50 food squad to be able to circulate
and organize the network of doors for
the midgame, allowing reinforcements to not be blocked by closed doors.. or intercepted by opposing dropped units (those doors give drops (using air transport units to circulate quicker on the map) an extra unneeded "buff"
and you would probably end up with a network of doors looking quite mathematical if you ever get to the late game
edit:
after thinking about it to death, i'm sure a cross between the two is advisable for optimum awesomeness for 1v1 ladder:
the door can be destroyed once, it has insane hp/armor (5000 5 armor)
you can gain (partial or complete) control of the door, it can be hacked (a ghost/infestor/templar or worker) by a unit indefinitely to open or close it through its menu, by the unit being geographically "connected to it"
ultimately (for late game) a worker could (with resources (min/gas/other) spent accordingly) repair/rebuilt the door
but that is just another not so well hidden old idea (that all three race could build walls without using buildings to do so...
so that two gameplays are accessible and both make sense all through the early mid and late game where priorities re align constantly
Again, this door business, even more than the destructible rocks, favor drop play for every race, favoring some more than others maybe just by the nature of the tech trees / race differences.
ps:
+ Show Spoiler +if anyone wants help to do such a unit you know where to find me