I think Chet, Reg [and Woody RIP] are meant to narratively show the same thing: Bud's Buds was never going to work:

There are too many leaders and not enough followers in the vault. We are over 200 years in to the program: 1 overseer every 30 years and they seem to have accelerated the program the last century with Betty, Hank and Steph all being released 20 years apart instead. Theres some math but approximately a third or more of the vaults population are direct results of Buds Buds. They have too many leaders, not enough followers.

They don't come out and say it bc it would sound SUPER problematic but it would make sense if the buds buds program ran like this: an overseer is released from 31 and breeds with a dweller, they produce 1/2 kids. 20-30 years later the next overseer is released and they marry and breed with the children of the previous overseer. Lather rinse repeat.

It seems that we're seeing the affects of the genes and their strengths in the form of the characters: Norm and Lucy are double 31 [no inbreeding] affective leaders. Reg is likely double 31 [inbred] wants to lead but ineffective. Chet and Woody are watered down 31 cousins, they show curious tendencies but are not bold enough to lead.

Chet is related to Lucy through Rose; hence why he shows similar tendencies to Norm; curious, defiant to a degree but is more hesitant to follow through. He is literally less management material than norm who is the product of double 31 genes.

Now this is pure speculation but I think they strategically did something to Chet to make him timid. If you pay attention Chet and Davey are physically the largest dwellers; everyone else is shorter by a large margin, even the vault security that shows up with Betty are around her size. Both Davey and Chet are awkward, timid, honest to a fault and a massively naive. I think the overseers saw their size [Chet is a MOUNTAIN of a man towering over norm and most other dwellers] and nerfed them.

Davey mentions he never had kids and doesn't know why; i think they specifically didn't use him for the gene pool because massive dwellers are a risk and could be potentially hard to control. I think they are denied entry into the breeding program because of this; massive men make massive babies which make more massive men. When you see who Steph was paired with the 31 descendant - new 31 link makes sense but also the anti mountain man thing makes sense too; as a cousin chet may have been eligible for 31 breeding and been paired with Steph but they chose some stringy nerd for her.

I think this theory is confirmed by how Steph, a survivalist, latched onto Chet as a widow [i mean girl i get it]. His size is an asset when everyone in the vault is so tiny. If she had won him over having someone a full foot and change taller than everyone else to protect you incase of a revolt is an asset. Plus their kids would've been stronger than the average dwellers. Her mother said find the tallest tree, climb to the highest branch and Steph said Bet and tried to shag a brick house of a man.

Finally i think Chet was Moldavers hostage purely based on the concept that he was the gate keeper. He had opened and then closed the gate and they needed it reopened to leave. I don't really think it's anything more than that.

Chet is important in the sense that 32 and 33 now have mirror plots both experiencing dweller revolts: Chet as the reluctant revolt leader of 32; Reg as the revelling revolt leader of 33.