I'm personally less concerned about the specific time to black belt. A lot depends on the amount of curriculum that student is required to learn and how much they train.
One guy goes to a one hour class twice a week for two years and that's 832 hours. Another guy goes four days a week and that's 1664. Still only two years, but oh what a difference between the two people. A third guy who makes five days a week for 2,080 hours of class in two years.
Also, you can spend four years in class and if you spend four years training like the typical hobbyist (90% of MA students), there won't be all that much difference between two or four years.
Since we're speaking of black belts in the general, I'll address taekwondo schools, which comprise the majority of "karate" schools in the country, and are probably the ones most responsible for the state of the modern black belt. Never mind that taekwondo isn't a ryu of karate, more than two thirds read 'karate' on the door, and to the general public, its all just karate anyway.
Kukkiwon taekwondo curriculum is pretty minimalist. You'd have a hard time pulling four years out of someone with just Kukkiwon curriculum. A good number of taekwondo schools add weapons and other curriculum to keep students interested after blackbelt.
Personally, I feel that the bulk of schools have collectively lost the ability to push the students to do more than just gear up for the next level belt test. That, and I know of few, if any schools in my area where anyone ever fails a colored belt test. In the years I've been at my own school, I've seen only two people in an adult class have to retest for a colored belt.
There is simply too much at stake for most schools to not pass a kyu grade student. To much in terms of money and such. Unfortunately, the kyu grades are the ones that should be the most diligently worked with and often, they're just seen as paying customers on the way through, expected to leave after they receive a black belt.
Another issue is that schools have a mentality that more is better. "We promote more blackbelts than anyone in the state" sort of mentality. Unfortunately, this actually attracts a lot of people for the wrong reasons, though I'm sure that its good for business.
Personally, I don't care how many blackbelts a school has. The black belt should represent a level of quality and a level of proficiency in the basics. I'd rather boast ten blue belts that are top notch than fifty black belts that look like yellow belts (yes, alarmingly, I've seen a few).
Daniel