CapnZapp
Legend
While I certainly am the last person to defend the CR system, they need some quick eyeball classification so you don't need to look at the stats to know a a Tarrasque is more dangerous than a Goblin.@CapnZapp
I mostly agree with your assessment (half level might be a bit low). I wonder though, where did the CR numbers come from in the first place? While there is something to the "must be this high to fight" element at lower levels, it quickly vanishes into insignificance. So why are CRs numbered the way they are? Why is the difficulty of an adult copper dragon defined as CR 14 rather than CR 20 or CR 8, or CR ZX-4?
So, for the purposes of quickly pegging a monster on a scale, CRs work just as fine as any other simple scheme.
I can even buy the idea "when in doubt, overestimate the monster". After all, one lame boring fight doesn't disrupt an adventure nearly as much as one TPK.
It's when people actually start believing the spiel about pseudo-scientific calculations to arrive at said CRs things go haywire.
The only thing a CR is good for is a very rough estimate. To downplay the "accurate science" BS, they could just have pegged each monster into one of the four tiers to really drive home the inaccuracy of it all.
But the idea of being able to use numbers to calculate a scientifically "correct" encounter is very alluring, and so the CR system sells PHBs, so it will probably always be included, even if it's all an illusion (avoiding the term "lie" here).