Many have 2 - one on the outside for "show" and $, one on the inside for "go". If you like it on the inside more power to you, I do as well. Not certain I see the value in something stretchy that would come into play after my shin/tongue mashed up against the hard plastic of the shell (strap on outside) - but different strokes and all.
The whole point of the booster strap is to let the upper cuff of the boot deform, which a traditional power strap doesnt allow, and to give the boot some more rebound during turn transitions. Having it on the tounge or on the shell doesn't make a ton of difference for me for the first one. For the second one it works better on the shell.
A lot of boots do come with strechy power straps now. The one stock on the dobermann 150s is nicer IMO than my expert booster strap because its softer and has better rebound when you release the skis.