Dave,
Well you are right that the cut grass can provide "free" nutirients, but that is not the end of the story. I have been using vacuums since the early 80s, but I vacuum under only 2 circumstances: (1) gathering up large volumns of leaves in the fall and (2) gathering up the grass clippings when I have had to mow the lawn when it was too tall.
The recommendation from turf specialists is that you cut no more than 1/3 of the length of the grass. So if you want the final height to be 3 inches, you need to mow when the average height is no more than 4.5 inches. When I can mow at this height, I do not consider vacuuming.
However, life is filled with lots of things to do besides mowing grass unless you are a golf course superintendent. During the past 2 months in my part of the country, we have had so much rain that the grass needs to be mowed about every 4 days. Many times I cannot mow for several days beyond that and when I do, the grass is maybe 6 inches or more in height.
If you just go ahead and mow this long grass without vacuuming, the long clippings lie up on top of the cut grass and do not settle in. Within a few days the lawn is covered with blankets of dried greyish or browinsh clippings. If you just wait a few more days and mow again, the mower simply blows these dried clippings all over the place. I see it happen with others all of the time. They spend the entire mowing season blowing old clippings from one side of the yard to the other.
The dried long clippings just don't "go away." The mower blades don't get a chance to cut the dried clippings up much because the air stream immediately propells them out the chute where they resettle on the top of the cut grass again.
This is the Major reason for me to vacuum---when I have to mow longer than ideal length grass. I transport the vacuumed clippings to a large compost heap on my property and dump them. Later I take material from this heap for flower pots, containers, and as mulch for the flower beds. Thus I am retaining some of the "free" fertilizer even though not as much as I would if I could simply mow no more than 1.5 inches off the top each time.
As others have stated, vacuums do not work well with wet grass. They don't work well in extremely long grass (say 12 inches), but they do work in 6-12 inch grass if you simply drive slowly enough.
Then you just hope that the next time the grass needs to be mowed will coincide with the time you have available to do it, and you won't have to vacuum.
JackIL