If you've expanded it in the hole, it may be hard to get out. To release some of the pressure, drill through (past the plate into the back side head, but not necessarily "through") with a ~1/4 drill. Then, either blunt/make a punch to span the hole, or work it from the sides, being careful not to dig into the material surrounding. If you do that (dig into surrounding), then it can make things worse, effectively "staking" the rivet into place. Good luck. They can be bastages.
And, you may be right about the equipement making it harder. I've got an old IR chisel with an 80 gal Curtis compressor. I run out of go long before it's ever even gotten warmed up. And it's STILL a total PIA on some of them. Others pop right out. As others have said, the blue-wrench can make it a lot easier/faster, and with some skill/finesse and the right tip you can take a rivet out without any real damage to the surrounding material. But it doesn't help a lot in tight spaces where you can't really control the action, and those are the same ones that are hard to remove mechanically, so with a few exceptions, I almost never do it that way.