I totally agree, as that is exactly how I work a bolt as well.

You know, one of the best and most reliable feeding/extracting/ejecting rifles I've ever used was a "tang safety" push feed Ruger in 300 Win mag.
It didn't come that way out of the box but needed some modification.
I used it a lot right through the 1980's, and also lent it to hunting clients on a regular basis.
It was super slick and totally dependable in all the situations that we put it through.
I foolishly sold it, and later replaced it with a CRF Mk11 stainless synthetic in the same caliber.
The Mk11 was accurate, fed well, and was reliable, but it wasn't half the gun my old original M77 300 mag was.