There are a lot of people quoting masters from the past who say a lot of bad things about this opening. They are almost always wrong. The Opening is 1. e4 e5 2. Nf3 Nc6 3. c3
I have heard that 3. c3 is a mistake because Black equalizes quickly with 3. ...d5 however that is not true at all. White responds 4. Qa4!
I have heard that the Ponziani Opening is bad because it leave a "hole" on d3. That "hole" lasts a very short time as White will very probably soon play d4.
Also said is the the 3. c3 move takes away the natural placement of the queen knight . So does the Ruy Lopez!
Also many masters have picked up one line in the Ponziani and have said that it was a dead draw. While this is only one line and there are many ways to vary--I have published analysis that really White has very good winning chances and how to proceed.
I could go on and on but, instead will give you one recent game.
this is a 15 minute per player game which I play on another format.