Ah, I've never owned a Moto Android, so this is probably a Moto-specific feature.
My alternative camera app (Open Camera) has a "touch to capture" option, though I don't use it: to me the natural use for touch is to select a focus point rather than take an image (though you can set it to require a double tap to take a picture, which does allow you to use a single tap to select focus point). It also has an on-screen zoom slider, but not an "anywhere on the screen" gesture. But you will find that any alternative app will probably lack some of the features of the built-in app too - I mainly use the default app, but like to have an alternative available (it's rare to find any one app that does everything better than another).
