Iron Dome was created because Israel had a katyusha rocket and arty problem being fired in mass by terror organizations of which Patriots or any other SAM system can't handle.
Just to clarify what was said above
Don't confuse Iron Dome and David's Sling, 2 different weapons!
Iron Dome is for as you mentioned, rockets, artillery, mortars (uses "Tamir" missile)
David's Sling is the replacement for Patriot for intercepting missiles and aircraft (uses "Stunner" missile)
David's Sling was developed to counter the modern ballistic missile threats posed by Iran, not small rockets. The same type of tactical missiles that leveled an American base in Iraq in revenge for the death of Solemani.
I cannot speak for everyone, but my mistrust of Patriot is from historical fact, not because the Kinzhal is a superweapon.
To paraphrase a former classmate of mine who had lived in Haifa, "The only thing more useless than the scuds were the Patriots"
Edit:
Here is a link, there are tons like it if you search. Factual and unrelated to Russian misinformation (and written well before this conflict)