You're already late for work.
Rushing won't help that. Speeding won't help that. Aggressively accelerating and slamming on brakes won't help that.
By the time I'm late for work, it's no more annoying than seeing it on any other morning where I'm still going to work, and still have to scrape at ice/frost.
Maybe it's just not my personal compounding annoyance, because I certainly understand multiple minor annoyances piling on making you pissed.
Lpt: boil water at night before bed, so you can use it to melt the ice off the windshield. Just pop it in the freezer to keep it until morning.