With that said, it is technically possible; however, in the case that pets did not disappear when changing areas, the cost of using that pet to its full extent would be increased (the cost of the jug).
I'm really confused as why they seem to feel a trade-off would be necessary here. Beastmaster isn't going to be viewed as overpowered anytime soon, and letting jug pets carry over between areas is a trivial cost savings- No price adjustment to jugs should be needed.