Yea, no. At my last job every project was constantly late because they kept over promising and clearly didn’t have enough people for what they committed to. I couldn’t even get a department meeting once a month for an hour because everyone was always “too busy”.

These projects always need everyone to commit to it like it’s a personal passion project because their goals are unreasonable. If they can’t handle someone being away for a day then the manager clearly cannot plan and/or the enployees need better training(in my case half of them were simply stubborn and ineffective on top of the questionable management). Sure, don’t take a week off right before a reasonably set deadline if the work’s not done but otherwise do whatever.

I had someone call me yelling because I was going to finish the job in exactly the amount of time I said it would take me, but I started a day late due to technical errors which made another project go over by a day(and that day I still stayed late to make sure things were done!). If you can’t take a day off then you also can’t be sick, and if managers don’t account for THAT obvious possibility then they are fucking stupid and awful managers, zero exceptions.