My understanding is that it is more a consequence of politics than the system... Sure you have a veto proof majority on this bill, but what about what comes next?
The governor is able to stop "tyranny of masses" by their veto power. Almost no bill in our partisan age is able to pass with a veto proof majority. So the governor has the ability to prevent good outcomes for specific members of their party in the legislature in the future. Sure a budget that makes the party and governor look good will pass, but members who "step out of line", will find that they can't "bring home the bacon" in terms of what is allocated to their district.
So could the bill be pushed through unmodified despite an governor's veto? Of course. The system expressly allows this given a 2/3rds vote. But the legislature needs to weigh their options:
1.) Have all members push the bill forward anyways
2.) Have just enough members push the bill forward
3.) Accept the governor's revisions and move the bill forward
4.) Drop the bill
As a representative it is hard to tell which of 1/2 you are choosing in the moment. The issue is that 2 may paint a target on your back. The members of the party opposing the governor are less incentivized to care about the veto. So do you want the governor to hold a grudge with "1 of X" representatives of their own party who sided against them? Granted the legislature is about 2/3rds democrat, so for a break with the governor to happen maybe half the democratic legislature would have to break with the governor.
3 Is appealing over 4, since you are able to claim victory for now. Something was passed after all, and the name of the bill alone is usually enough to make a good ad come re-election. and if the issues really are so severe, this is just another victory for the future you.