I think one of the issues here, is the acceptance that a Very Important Job means that the man (usually) doesn't need to share the childcare drops & collects & corrosponding 'work'.
There are so many threads on here where women have taken on the lionshare of the DC 'management' during the week because of these sorts of jobs.
I have seen it in RL too. DH's that have to leave before childcare & return once the kids are in bed. I am afraid there is part of me that wonders if maybe suits them to not be around.....
I do know that there are well paid jobs that are given with "expectations" of a level of work/committment/presentiseem.
However, equality in the workplace would move along a bit if those with VIJs started visably sharing the childcare drops/sick leave.
In the book Shattered, which is about inequality in the workplace & parenting, the author found that men did work flexibly (going to sports day etc) but they just didn't tell/ask anyone. Whilst women typically go by the book and request the flex hours etc.
It just made me think if only men would be more open, then flexibility would be seen as the norm etc.
So, back to the OP. I would suggest that he does consider it, but with the agreement he'll do half the childcare drops/collects & sick cover..And that when he travels he needs to then cover a bit more when back, so you stay later at work etc.
I do think staying in one company for such a long time isn't great. So moving would be good, but not at the expense of your career.