This has been known to bug me whenever I brush my teeth…
In what way does squeezing out my toothpaste from the bottom of the tube afford me better results?
and
Exactily how much better are the results from doing so?
Obviously you do not have to buy the toothpaste in your household.
By squeezing from the bottom, you eventually get more of the contents out.
When tubes were made from the thick aluminium foil it was not unusual for he tube to split partway up which resulted in a significant portoin of the contents being thrown away, by squeezing from the bottom and rolling the empty part of the tube up, this was less likely to occur.
…and all these years I thought that squeezing from the bottom aided in better oral hygiene, but it is merely a solution to the toothpaste tube design flaw. Why bother printing such a notice?
And now that nearly all tubes are plastic, it doesn’t make much difference. Yes, you can get maybe 5% more out that way. Big Whoop.
Note that I guess there still could be some odd toothpastes with stripes & such where it could make a real difference.
Interestingly enough, the new Colgate Simply White whitening toothpaste has instructions: For best results, squeeze tube from the middle. This is because the cap (and presumably the tube) are divided in half; Toothpaste comes out one half, and whitening agent out the other half. If you squeeze the tube wrong, you will not get toothpaste and whitening in equal proportions.
For a look at how much toothpaste is inside a typical tube:
I remember seeing a gadget years ago, in the days of the foil tubes, that let you get all the toothpaste. It was a ceramic block with a slot into a cylindrical hole, and a slotted cylinder to fit. Put the base of the tube into the block’s slot, slide the cylinder in to grab the fold at the bottom, and twist to dispense.
The reaction I most often heard was “What a great idea!” but I never saw anybody actually use it.
As an aside, most people use FAR more toothpaste than they need to. Running a heavy bead of toothpaste along the length of the brush head as shown in commercials is totally unncecessary and wasteful. You need only a pea-sized amount to do the job. I’m sure the toothpaste manufacturers would have you believe otherwise. 
We actually had little gadgets like this when I was growing up, except that ours were made of plastic. We really did use them. As others have pointed out, though, now with plastic tubes, they’re really unnecessary.