Push and shove will never be an autorouter. Both have their uses. Experienced designer don’t like autorouters.
What is really needed is for a competent programmer to port freerouting to another language. Java is getting some problems thanks to Oracle. This programmer had better live somewhere away from the Zuken lawyers.
I was not ready tonight to write a wall of text or start the first paragraph of a book; so pardon my earlier “sum up”.
It appears if KiCad developers are looking to include “pin-swap” from PcbNew as well as maybe doing a “drag” of existing board traces in future versions. I speculate that KiCad will still call it the “Push/Shove Router” even with these extra features in the future versions.
When I first downloaded a V3 of KiCad I used the FreeRouter at the time for several attempts to route traces on a simple board. Even then it was obvious that, me (as a human), could do a better at the trace layout. Maybe because I’ve always like mazes and puzzles as a kid?