Generally I think the system is good, but for the most blatant incidents three points is not enough in isolation. Think of Vettel at Baku 2017. You would need to make four infractions like that before getting banned.
I think the maximum should be increased to six but of course, anything from three to six should be given as sparingly as of now.
Here are the incidents there has been 3 penalty points. I give my verdict on those and which should have been more.
Maldonado - 2014 Bahrain - collision with Gutierrez
Clearly Maldonado's fault, but the crash was really more spectactular than the intent so I think 3 points is OK.
Ericsson - 2014 Italy - speeding under double yellows
In this kind of infraction I could see three points being the norm, causing further incident would then be worth more.
Maldonado - 2015 Malaysia - speeding under safety car
The previous applies to this as well.
Vettel - 2015 Canada - overtaking under red flag
He had quite a lot of speed there. This was quite close to the incident zone IIRC, so maybe 4 or 5 points.
Verstappen - 2015 Hungary - speeding under safety car
See above.
Räikkönen - 2015 Russia - collision with Bottas
Clearly Kimi's fault but not too malicious, 3 points is OK.
Kvyat - 2016 Russia - double collision with Vettel
Maybe two points each so 4.
Gutierrez - 2016 Belgium - Impeding Wehrlein (?)
Don't recall that incident too well, happened in the Kemmel straight IIRC.
Grosjean - 2017 China - speeding under double yellows
See earlier part of the post.
Palmer - 2017 China - speeding under double yellows
Ditto.
Vettel - 2017 Azerbaijan - Dangerous driving
The intent was stupid, so I put this one on 6 points.
Massa - 2017 Belgium - speeding under double yellows
See earlier
Räikkönen - 2017 Belgium - speeding under double yellows
Again.
Perez - 2017 Singapore - speeding under double yellows
And again.
Ericsson - 2018 China - speeding under double yellows
And again.
Stroll - 2018 Austria - ignoring blue flags
There was some team radio message behind this so I say this served right.
Hülkenberg - 2018 Belgium - start collision
Pretty awful mistake, I raise this to 5.
Perez - 2018 Singapore - collision with Sirotkin
Intentional contact, so 6 points.
Ocon - 2018 Brazil - collision with Verstappen
Ocon was a lap down but the collision itself wasn't that bad so I keep it in 3.
Vettel - 2019 Italy - Collision with Stroll
Basically this included dangerous return to the track and the collision so I put this one to 4.
Russell - 2020 Britain - speeding under double yellows
See earlier.