Captains are in charge of the safety of the flight - commercial delays are not within that remit, but are down to one of the company's commercial managers. Like it or lump it.
Actually, that kind of depends on the airline. Some operators recognise that the people at the coal face actually will understand the likely ramifications of any delay and whether it is likely to be absorbed in the next sector or not. Other operators treat their crew like brain damaged idiots. Its a classic failure of leadership to fail to delegate an appropriate level of authority.