I agree about the load-bearing structure of the secondary hull, but I'm in the YMMV camp as the low power phaser hits from the Reliant appear to be only "skin deep".
If they were penetration, there would be hull breaches in the engine room area and the the Enterprise would've been sliced through in half at the the torpedo bay.
I disagree. Remember, you're talking about a complex structure, not a "solid mass" in any region.
Think of, for instance, the structure of a typical office building. There are exterior walls, which have a degree of load-bearing capacity but which are not primary load-bearing elements. You have a steel infrastructure that carries the majority of the load, often a composite infrastructure consisting of steel with concrete poured over it.
You've seen what happens to such a building when there is significant damage. The walls and so forth are perforated, and sometimes the concrete is blown off of the steel infrastructure, but the building will continue to stand, until the primary load-bearing members are too compromised.
Think of the sequence in the movie True Lies, where the helicopter and the Harrier are in combat downtown. The aircraft weapons systems basically shred, front to back, the building internals (including the villains) but the building's structure is still there.
That's how I see the hits in ST-TWOK. The phaser strikes blew through the hull plating, through internal bulkheads, and compromised (but did not "destroy") internal mechanical load-bearing elements. Certainly, anyone in one of the external compartments, where the phaser strike hit, would have been incinerated. The energy of the blast as it dug deeper into the hull was decreased, until, by the time it hit the Main Engineering compartment in the core of the secondary hull, the energy had been dissipated enough that the crewmen in that area were, in most cases, able to escape with their lives.
Clearly, the ship has a tough "skeletal" structure, and probably has some self-healing systems (as well as some great repair crews). Also, the flick was done on a very tight budget, and doing the "crewmen being sucked into the vacuum" shot wasn't necessary to communicate the idea that the Enterprise was getting the... snot?... kicked out of her!
The surface hits did penetrate deep enough to cause some internal damage (like to the main energizers and one of the torpedo rooms) but further viewing shows intact structural pieces and relatively little damage on the surface of the ship, IMHO.
All we really see, in TWOK, is that they did a quick cosmetic dress-up on the ship with stuff that could easily be cleaned off.
Interestingly, in ST-III, we see damage repairs (scorched areas, patching, etc) that we didn't see in ST-II. If you look at that film, and pay attention to the hits that Enterprise took in ST-II, you can only conclude that some of those hits totally perforated the hull, from port to starboard!
Ripping away the 23rd-century equivalent of "sheetmetal hull panels" and "internal bulkheads" does is basically what we saw there. (Had the ship had shields and screens up, they'd have been safe enough, of course.) But we know where main engineering is, and we know that it's a couple of dozen yards away from the outer hull surface. A number of compartments, outside of main engineering, has do be destroyed in order for the residual energy from that blast to make it there.
As for the port torpedo room... well, there are inevitably going to be some massive load-bearing structural members in the dorsal. It's a safe bet to say that the port room was rendered uninhabitable by the hit there, which basically ripped that area open like, as the SFX team described it, a "can-opener" effect.
(It's pretty clear that they intended for there to be two launcher rooms in the neck. There are some scaling issues associated with that, of course... but in the "Spock's tube is launched" sequence you can see that the port launch tube is still destroyed... and that Spock's tube is launched from the starboard side (which, unlike the port side, was mostly undamaged).
It's a fair assumption to think that the "fire" we saw was actually in the starboard room... and that the port room was totally decimated by the Reliant's hit.
A more severe example of heavy damage would've been the Constellation from "The Doomsday Machine" with the twisted nacelle pylons, etc... but she still held together under Kirk's bad impulse driving

But even in that case, there was no mention of SIF or the need to re-establish it even with that kind of damage and power loss...
They didn't mention it... but that doesn't mean it's not there.
Of course, we also saw the AMT-stellation vibrating and shaking and the nacelle "bobbing "in some shots... which sort of infers that the ship is barely holding together and is about to shake apart. (They even replicated some of that in the remastered version!)
Was the Constellation about to just fall apart? If not... what was holding her together? I have no problem with the idea of a SIF, or SIF-analog, being present there.
But, again, we need not treat this as the same "all-inclusive" system that they have in TNG times. Maybe, instead of being in every frame and stringer and plate, it's just there in certain key locations during the TOS-era?