This is where actual probabilities come in: if you give me 90 % probability ranges (i.e. you think there's a 90 % chance the actual time taken will fall inside the range you give me) that provides me with three extremely powerful tools:
1. First of all, I can use Monte Carlo techniques to combine multiple such estimations in a way that makes sense. This can be useful e.g. to reduce uncertainty of an ensemble of estimations. You can't do that with fuzzy labels because one person's range will be a 50 % estimation and someone else's will be an 80 % one.
2. I can now work these ranges into economic calculations. The expected value of something is the probability times consequence. But it takes a probability.
3. Third, but perhaps even more important: I can now verify whether you're full of shit or not (okay, the nicer technical term is "whether you're well-calibrated or not".) If you keep giving me 90 % ranges, then you can be sure I'm going to collect these and make sure that historically, the actual time taken falls into that range nine out of ten times. If it's not, you are overconfident and can be trained to be less confident.
The last point is the real game changer. A point estimate, or an estimate based on fuzzy labels, cannot ever be verified.
Proper 90 % ranges (or whatever probability range you prefer) can be verified. Suddenly, you can start applying the scientific method to estimation. That's where you'll really take off.
To be honest I still don't really think any of this stuff can be truly verified beyond actually doing it or having a very well understood set of requirements that have been worked against plenty of times before.
About verification I think you're right in a very specific sense: you clearly cannot verify that any single estimation is correct, range or not. However, meteorologists and other people dealing with inherent and impenetrable uncertainty have found out that a historic record of accuracy is as good as verification.