To begin with a general defense of walkers, I'm going to point out that since the advent of warfare, the single most deadly combat machine has been the human, a light biological bipedal walker.There's also some new points I want to bring up. A tank can carry a very heavy gun. An AT-ST can't. Perhaps for conventional cannons it's not a meaningful advantage, but once railguns come along they'll be a big deal. Also, an AT-ST can't cross very uneven terrain with small elevation changes because the feet of the AT-ST can't readily grip the ground. This is no problem for a wheeled vehicle since you are naturally stable and don't have gripping problems as severe.
It is deadly because it is highly versatile, able to retain limited functionality even after substantial physical damage, and has practically unlimited tactical flexibility. Humans can cover terrain ranging from extreme mountains to swamps to the most dense underbrush to swimmig underwater, and can conduct combat missions within these environments with a broad variety of modular equipment extensions.
The general idea of a walker is that of a mechanical version of a human or animal, borrowing from nature's proven designs. To build, in other words, a superior version of a human, so far as this is practicable.
So, shall we?