As far as the "Yikes" goes, I'll offer a counter point...
I grew up in Northern Colorado and was back last year for five weeks including several weekends cycling. I was in Boulder but cycled mostly east of there in region of Longmont/Erie/Lyons and made brief foray up to Fort Collins.
It does depend what you compare it to, and I think overall roads in northern Colorado are better for cycling than roads I have here around Austin. Strava heat maps will show you quite a few folks riding in the area as well as common routes. There is mostly a grid pattern of roads some paved and more unpaved. The population in CO and in the area has grown a low percent a year (growing up Longmont had ~25,000 people; it has had over 100,000 more recently). There has also been a proliferation of subdivisions/developments including through Weld County/Boulder County and along the general corridor. Some places the roads haven't always kept up, but it is a bit of hit/miss because other places they've put shoulders in. Erie is an illustrative case study. On one hand, former "county line road" had become busy and they haven't updated the shoulders (yet, there is a project in planning -
https://www.coloradohometownweekly.c...nty-line-road/). Similarly, growing up there wasn't as good an alternative going between Denver and Boulder but for at least a decade there has been a pretty good Denver/Boulder bikeway. I don't always go for there sorts of bikeways touring, but now in that area these are becoming better alternatives.
However, at same time, there is an interconnected network of trails going up through Erie. The trick is finding and linking some of these combinations. In general, it seems Colorado roads are more likely to acquire shoulders than Texas roads as development happens.
With all that said, depending on where you are going in Nebraska, you don't necessarily need to go via Cheyenne. You can also follow the Platte River valley out through eastern Colorado or head first to Fort Collins and then east out CO 14 towards Sterling.