I can easily think of at least a million reasons he'd take the WSU job, as that's about how much I expect his salary to be increased. Kelvin may retire if he wins a national championship, but otherwise, I think he's looking at least 2-3 more years, which could easily turn into 5. Kellen has been an assistant there for almost a decade, so I can't imagine waiting another 5 years when you know you're as ready as you'll ever be.
As long as Kellen can maintain 20-25 win seasons at WSU, the UH job is likely his if he wants it in 3 years. That shouldn't be hard to do in the AAC, which is getting weaker and will artificially inflate their record. If he wasn't going to be able to do that at WSU, there's no way he was going to be able to keep his job long at UH in the Big XII. Given the time he's spent at UH already, it's unlikely a couple more years in the area will bolster his recruiting or help him grow as a coach. He can develop new recruiting relationships in Kansas and surrounding areas, and regardless of how well he does at WSU, he'll be better prepared to take over at UH.
The other benefit of WSU is that it would give him credibility for doing something outside of his father's shadow. It would give him more credibility with recruits and drive up his salary at UH. They may guarantee him the UH job after Kelvin retires, but that may only mean a 1M salary. A few 20-25 win season at WSU quickly bumps him up to 2M, and if he has a 30 win Sweet 16 year prior to Kelvin's retirement, he could take over at closer to the 4M price point his father is commanding.