Their job is to stop the aid so ofcourse they would try and intercept or attack from behind the enemy army moving to aid Han. For you to get past them in time and have enough man power left to make a difference in the upcoming battle you will need an army of over 100k at the very least.
Mou Ten's forces have to take to the field to stop Zhao reinforcements from making it to Yellow River. Ba Nan Ji and Shun Sui Ju don't need a 100K army to get past the Gaku Ka.
Likewise, there is no need for a 100K army at Rakushi. Go Hou Mei is unconcerned about retaking Rakushi, be it now or later, likely because he's good at siege warfare. If he does bypass it without taking it, the Gyoku Hou might chase after them, which would work just as well in his favour.
Zhao has already lost armies in the 100's of thousands in the past couple of years so makes sense that they would try to sit this one out and try to rebuild strength and enjoy their victory while Wei waits and sees which place they should attack depending on the situation and how the battle unfolds.
Ri Boku has explicitely stated - many times - the Qin are the greatest threat to Zhao. He has also spoken multiple times on the importance of destroying their ambitions for unification.
If they went and ensured the Qin lost another 100K army in Han, they would be finished.
He's ALREADY planning on engaging, it makes no sense to wait when having overwhelming numbers will only help preserves lives in the long run.
If Han were to suffer huge casualties and another state wished to take advantage you could move your army and stop them then.
They don't have standing plans for attacking the Qin in Han if they were confident in a Han victory, never mind a crushing victory in which Han preserves most its strength.
Also if Wei were to reach and support Han wouldn't that just make Qin retreat and maintain their strength?
It's better for you to let them battle it out and then steal territory from an even weaker Qin.
It would be a win-win regardless.
If they go and manage to catch the Qin while they're engaged, it's a massacre.
If the Qin retreat, they'll suffer another failure, another hit to morale, loss of investment in the campaign so far, and they'll have Han in their debt.
There is no downside to going as soon as possible for anyone other than maybe Wei who are after some more Han territory - which they could negotiate as a condition of their support considering Han a) is in a fight for its life, and b) is used to giving up territory to fight another day.