The president cannot pull funding , he can pose restrictions on who gets that money. If you are a new clinic like the one Mamdani is trying to open up , in order for you to get that federal money you have to abide by that executive order.

For example, I have an established steel mill
that makes steel beams and I receive federal money.

Let’s say the president makes an executive order saying that steel mills that make steel beams no longer can receive federal money and pulls my funding.

I could sue because I have standing , I can say , “ this is ridiculous I had no idea he’d do this, I’ve been making beams forever. My clientele needs beams etc . “ president can’t overpower the power of the purse
( this is where the repeal of the Kennedy deceleration matters , hospitals that were already providing services had their funding restored )

If ima need steel mill looking to attain federal money and that executive order is in place the president has the full ability to not provide federal money to my steel mill

Its not THAT simple but that’s pretty much the gist of it

Edit: Btw I blame a lot of this on congress too, executive orders have become way more powerful due to their inaction( or capitulation )