I worked for a lot of airlines(not by choice, lot's seem just to die over the last decade) and different a/c types.
Some had 1 tiller, others 2.
On this with steering both sides the FO could drive on his sector. But to be honest, this was one company and all the others sticked with "the captain drives".
I find this fair enough as the captain(and not the FO) is responsible for the safe operation of the flight and even more for safe taxi procedures. If something goes wrong, even initiated by the FO, they always go for the guy in the left seat.
Best example - in my current company we do as well lots of flights into Africa, had already a few "wing touches" on narrow parking areas while under control of a marshaller. He waived them right into the obstacle and of course they made the captain the black sheep - even changed procedures so captains would be even responsible for damage caused to the aircraft while under marshallers guidance. In this case I prefer to drive the thing into the wall by myself rather then let the FO do it
.
The same goes for a Rejected TO. I see(like most companies) no problem why a FO could not call out a malfunction, but making a STOP or GO decision should be(and is nearly everywhere) the captains decision. To many "opinions" during such a critical phase can cause confusion and lead to errors where you do not want to have them.
The FO has a very important role on a flight deck by supporting the captain and giving ideas. Sometimes as well to bring the captain again on the right track if he took the wrong turn or missed something.
But Go/No Go decisions are very tricky and need a lot of experience.
The only eception from above said things and the copilot may actually rightfully reject are jammed flight controls on his sector. No way that the PNF would figure that out and here it is absolutely the FO's call to reject.