it struck me more the way he so easily pressed the button this time around. At the time I was actually kind of put off by it, how easy it was for Ten II to do it

Me too. My reaction was 'but...but...the Doctor wouldn't do that.'

Which is precisely why the had him do it. To illustrate that there was a difference between them (hence the whole needing to be fixed by Rose).

But it's true. SOMEone had to do it. And the world is, no doubt, a better place for him having killed them. Same as when Rose killed them all.