As for the OP’s question, some TM’s and Planners might give you the odd expletive when you tell them you’re still waiting at a delivery point or stuck on traffic and aren’t going to make the delivery, but my experience its not personal, just another problem to add to that days list.
The main thing as has been covered is as soon as you know it not going to plan, inform the office, same as running out of hours, then its easier to change plans.
I know somebody said don’t give them options, but that really depends on who you’re talking too, far to many operations seem to be drivers vs office, but if I think of a solution I will give them that option, but its their call.
As for knowing whether its genuine or a driver taking the ■■■■, I’ve also worked in the office, and you soon work out which drivers just get on with it, minimum fuss and those that need checking on and those the are just incompetent and respond accordingly, might be even easier with trackers.