In high end phones pictures are taken continuously while the camera app is open. When you tap it saves the last one taken from just before you tapped, so there should be no motion blur from the tap itself.

If that's not working, you can also tap and hold which will take a burst. All the burst images will be saved, but modern gallery apps will automatically find the least blurry shot so you don't have to.

Most modern smartphones also support camera voice control. But if course that introduces an additional delay and can be awkward in some settings.

Practice resolved the issue for me. That's consistent with pretty much every aspect of photography in my experience: the more pictures I take, the better I feel about the average result.

Makes sense. It'll be more of an issue for the older or less healthy or just genetically unlucky.

I am glad that Sony Z5 has a camera button, it is much nicer and more natural to use than trying to touch the screen

You can use the volume (-) button on iPhone.

It's still in the wrong place, balance-wise. The camera button should be as close to the edge as possible so that the thumb can counteract the depression force; otherwise, the picture may come out blurred.

Volume up also works.

My Lumia 950 has one as well.