I don't think that's something really that unique to Republicans (also for what it's worth red/blue only became associated with Republicans/Democrats in the 2000 election and previously the Republicans used blue in their party's branding, but that's besides the point) as there are plenty of places that have been Democrat strongholds for decades that are in just as bad of shape (do neither sides economic policies work?). The real crux of the problem is that when any one party maintains control to that degree or has no real challengers, they have no incentive to do better. We look at something like the Comcast or other cable monopolies and see how shit the service is so why do we expect something different from political parties?
The stupidest part about it is that the first past the post voting system all but ensures that we see this outcome. I don't mean to say Democrats and Republicans exactly as you see them today, but two parties that are becoming increasingly polarized as there's no real room for anything in the middle. We've seen it historically in that the United States has always had two dominant parties with any third party being little more than a flash in the pan or one that eventually cannibalized an existing party and took it over. Were this to happen frequently enough, the system would be better, but the existing parties have been around far too long and with the exception of the crossover during the civil right's movement haven't changed much at all.
We need a system where it's possible to have more than two parties because it will allow people to find something that's a better fit. If you want both the right to own a gun and to have an abortion, there's really no viable party for you, but with a system that isn't first-past-the-post, it becomes possible for those more nuanced parties to exist, which means the existing parties lose their monopoly status and have to be more responsible to the voters instead of to a small number of moneyed interests.