Exhaust port was a quick fix for big problem, it had to be operational, especially during the firing sequence
As we all know, Galen Erso deliberately sabotaged reactor core, ostensibly to reduce weapon recharge time, but in reality to make it unstable. Here is excerpt from Rouge One novelization
Document #YM3884M (“Reply to Waste Radiation Distribution Solutions”),
sent from Galen Erso to Engineering Operations Manager Shaith Vodran.]
Sincere apologies. I fully agree that this is unacceptable. The
modifications are intended to reduce primary weapon recharge times to
satisfactory levels (I’m sure you saw Tarkin’s directive) but sloppy
work is sloppy work.
I assume you alerted Director Krennic to the report as well?
More as soon as I’ve spoken with my team.
He then "offered solutions", but only No 3 (exhaust port) was feasible in allocated time, which he planned all along .
I alerted the director personally, at your suggestion.
I also spoke to my team and we identified the problem. The reactor
core modifications are resulting in radiation buildup, which in turn
has the potential of interfering with the hypermatter annihilator.
The buildup is caused by the inner shield actively reflecting excess
particles and metaphorically “cooking” the reactor core. Had the
shielding team’s research not been so heavily compartmentalized this
might have been avoided.
The reactor core modifications must remain as-is. Therefore, we are
left with three possible ways of avoiding radiation buildup.
Option one: construction of a particle funnel and recycler. This is
known and tested technology. I am confident it will function. Physical
requirements mean the recycler would need to replace existing
noncritical mechanisms under the northern command sector, but I
estimate the needed disassembly would take under two weeks.
Option two: further refinement of our reactor technology to reduce
waste particles. I have several team members keen on this possibility.
They are excited about the potential for a technological breakthrough.
Option three: construction of manual venting shafts and thermal
exhaust ports. This should reduce particle buildup to within
tolerances but not to a degree I find personally acceptable. In
addition, adding venting shafts risks additional incompatibilities
with noncritical systems.
Please alert me if you have concerns.
Krennic, as expected, selected quick and dirty modification
[Document #YM3884R (“Reply to Particle Buildup”), sent from Advanced
Weapons Research Director Orson Krennic to Galen Erso.]
New research and technological development is out of the question at
this juncture. Work up a full proposal for the exhaust port solution
and send the plans to Vodran for SSCR.
Even when fully opened, exhaust ports did not eliminate problem completely
[Document #YM3884S (“Venting Shafts”), sent from Engineering
Operations Manager Shaith Vodran to Galen Erso.]
What is this trash? The Systems Safety and Compatibility Report quit
running after two hundred redlines. I only reviewed the first dozen,
but it looks like you’re flooding half the station with radiation?
I thought these venting shafts were supposed to solve the problem.
No changes are approved.
Of course I should have warned you that your droids might register
dangers. The venting shafts are designed to expel the majority of the
heat and particle buildup, but some radiation leakage is inevitable.
We estimate that human crewmembers stationed in any of fifteen
sections would—in the event that the battle station fires the primary
weapon three times within one hour—be placed at increased risk for a
wide variety of long-term health problems. The SSCR, of course,
detected this in those “two hundred redlines.”
So, as you can see, Death Star reactors and exhaust ports were deliberately made as a sloppy work and barely held together as it is. Closing exhaust ports (even if possible at such short time) would have killed half of Death Star's crew even without Luke's intervention. Therefore, it could not be done at that time.