Takeoff roll is a very critical phase of flight, where correct decision to stop or continue should be made promptly and there is no time for discussion about it. Generally the captain has the most experience on the flightdeck, so they are normally the most qualified person to make that decison. Plus, ultimately responsible for it as well. To me it makes sense that captain has hand on the thrust levers during takeoff once takeoff thrust has been set, even though I am a big fan of "PF handles aircraft from parking brake release to parking brake set" (where flight deck configuration allows).
In my UK airline (B744) when the copilot is operating the sector, after engine start, we had complete role reversal. Copilot taxying. Handles thrust levers on take off and calls stop if necessary, loss off control, blocked runway etc. etc.. Captain of course can countermand at any time.
Are copilots in some airlines not experienced, or fully trained, in all aspects of the operation?
Forgive the ignorance, but are your copilots not fully trained in talking with ground staff during pushback and starting the engines?