I felt myself getting angry that Rupertus kept refusing to get the Army into action
There is a good a reason not to throw a green National Guard unit into the teeth of the Japanese or to rely on them. And that's the 27th ID from Saipan. Bill and Seth's narrative of the Battle of the Smiths is too focused on countering the original narrative from Holland Smith to fully consider that the 27th actually did fail to preform and Holland Smith wasn't Satan incarnate. It's narrative that's popular now, and no doubt helped by Holland's own words in '46, but it lacks a fair critique of Ralph Smith and the 27th, You'll notice in that episode Holland is often called to task for being the corps commander and having ultimate responsibility, Yet Ralph Smith is only lightly chastised for allowing his battalion and regimental commanders to do what ever they want. One time even praised for sending a sternly worded order to the 106th's CO. Yet this narrative places the onus on Holland, as the corps commander, to fix the 27th's problems and almost hold their hand. Note little is said of the 2nd and 4th MarDiv, who are relegated to back ground props for Holland's war with Ralph.
The 27th made two big errors IMO that got them on Holland's shitlist and exposed them as a liability more than the assault on Hell's Pocket. The first was the Battle for Mankin. While the Marines of V Corps hit Tarawa, the 27th hit Mankin the same day. I'll let the troop strength thingy from Wikipedia explain why it was expected it should have been quick.

And I'll post this video on why Ralph Smith's plan was
needlessly complicated, slow, and cautious from our favorite good Australian youtube historian. It is important to note here that Holland did not want to be on Mankin. He requested to be at Beito with his Marines. Turner (IIRC, maybe King) denied it and compromised he could land at Mankin. At the end of the first day, Holland is hearing the reports that his Marines are on the verge of being thrown into the sea, and he has a whole division that he could land as reinforcements as soon as they mop up 400 green Japs on a speck of land and
they're taking their godamn time. It would take them longer to take Mankin than the Marines to take Tarawa. This simply is not how you fight a war in the Pacific in '43.
The second is the final charge of Saito at Saipan. The 27th was supposed to close off the last Japanese pocket, but they never buttoned up their lines and left a 100 yard gap. And that gap was directly north of 10th Marines, an arty unit. The Japs didn't overwhelm the 105th and then hit 10ths Marines, a detachmant walked right past the Army (Who didn't even bother telling 10th about the gap) and directly to them.
And I'm not trying to shit on the 27th just trying to set the scene, but I have to correct another point from UHOTP. Was Holland a 'combat commander'? No, not really. But he was a fantastic officer who distinguished himself as serving vital but undramatic roles since Bellalu Wood. Despite the USMC's self made image, they do actually value officers who can accomplish things outside of quips and leading bayonet charges. Holland would pick up the small moniker of 'Father of Amphibous Warfare' and was chosen as the first Marine to hold a Corps level command for a reason. He's not some blowhard, his word carried a lot of weight in the USMC. And if he says untested NG units are a liability, which he has good reason to, people listen.
Anyway I could go for ages on this, point is the Marine commanders had very good reasons to be wary of throwing in the green 81st into the battle besides pride and obstance.
If you want to get into it,
I suggest this book. It's one of the first books to turn against Holland but unfortantly goes so far against him it actually makes the 27th look worse. A lot of the narratives of the Battle of the Smiths now seemed to have started there.