In my mind, rank progression provides two things 1)a motivational opportunity and 2)a goal to aim towards peaking for. As you get higher in rank (and 1st/2nd Dan isn't high rank) the gradings get further apart for motivation, but you should still aim test when the time limits have been met so that you are working hard to be ready at that time (peaking) and therefore improving your overall skill level.
In the color belt levels, definitely, when the students get to 1st Dan they should start to have a bit of independence and be able to motivate themselves, it's a continuous improvement process that you should be working hard throughout. Black belts that can't motivated without having an immediate goal ahead of them such as a promotion tend to lose interest, it happened to me after I was a 1st Dan and I ended up leaving. It wasn't until I got older that I realized how short sighted and impatient that was.
I think if a 1st Dan waits for 6 years to test for 2nd Dan, they have either been coasting and not really training hard during that time; or they have been, but just aren't as far along with rank as they should be.
If they are in a system that promotes in such relatively short periods then yes, if not then it doesn't mean anything.
Particularly, 1st-2nd Dan is just a filter period - do people quit once they've got their coveted black belt - or do they then knuckle down and get ready to go further. It doesn't take long to find out what kind of person they are and when you do, then move them on (either way).
Each to their own though...
A 1 year filter period is not much time to separate the quitters from the knuckle downers , if they only have to wait one year then the quitter types might say, "Well it's only 1 more year, I'll quit after 2nd Dan" and those who will tough it out for a few years and stay motivated without that immediate goal, I believe, will be the stronger for it.