To be honest, after a lot of trying and failing when it comes to "using things" to improve my riding, I've come to the conclusion that good old hard work is the most foolproof method. I've never tried this, so I could be talking a load of rubbish, but I would think that tying stirrups to the girth would make riding very awkward and really restrict leg use. I ride my horse through my legs more so than my hands and I'm constantly having to move my legs to ask my horse to bend and so on.
Personally I think that practising the hard way to lead to a more natural development of still legs, but I suppose that if someone was having real problems - say, the horse was interpreting the leg movement as an aid and speeding up, causing the riding to lose control or something.
Like the person above said, standing in stirrups is good for obtaining a more secure position, and is a lot safer than tying the stirrups to the girth.