It's certainly possible, though the main reason not to seems you'd have to modify the way you operated it, and it might not work well.
If you watch this chap, he relies on the strap being grippy enough not to move, and pulls down on the neck to operate the mechanism. As you are already gripping the neck when playing, it's easy to incorporate the extra movement required.
https://youtu.be/KhB2o1BeLNU
With the mechanism operated from the end strap button, you'd somehow have to push down on the guitar with your arm. Whilst you've probably got your forearm resting on the top edge of the guitar, pressing down with enough force to operate the bender whilst still playing could be tricky and a bit painful.
Then there's the question of leverage, so you'd still need a similar length primary arm, and the spring would need to be shorter and correspondingly stiffer. You may need to add in some gearing to keep it physically small, which will add extra resistance.
With today's CNC machinery, it's probably very feasible to make something compact that would work (though you'd need a different final mechanism for Fender style bridges compared to Gibson style bridges. But it might just end up too awkward to physically operate.
