Except his problem cases are in 2000+ elo.
This reaction is expected, because the common opinion of this is that Shaco sucks, when he factually is really strong. When the argument is "he's really bad, why nerf" I can't discuss that because your argument is based on something that's just not correct here.
I understand that high skillcap champions are powerful when highly skilled players use them, but balancing for 2000elo players is a lot like only balancing for 1% of your entire userbase, or whatever the percentage is. Most of us will never reach that 2000elo spot, which is probably the cause of the backlash.
Shaco might have a decent amount of health after his clear, but he certainly doesn't clear very quickly.