‘Thats the job of …’
It's the job for all of the crew - check the engine parameters; the professionalism in being able to contribute more than just required by procedures. To look at the speed trend - and with experience build a deeper awareness of what is ‘normal’, associating that with the felt aircraft acceleration, the sound of the engines.
These questions and events identify with the weaknesses of SOP compliance - there is only one way to do ‘it’, stick to the rules, don't deviate.
The reality of operations is that adaptation is required, to add more than might be considered in training; the small, innocuous, apparently unimportant issues which at the end of the day avoid an incident or are just that feeling of a job well done.
Wet and windy; some aircraft require the relative engine thrust levels to be checked during acceleration - just to retain control of the aircraft.