If you have set yourself up to specialise in direct annexation, mass vassals, reduced tech cost, the effect of a poor ruler can be more or less negated. However, I agree that particularly early in the game or if you are expanding in manner your country is not well suited for then a 0/0/0 will have significant detrimental affect vs a 6/6/6.
Earlygame is the worst and most damaging by far, because often 50+ power projection isn't realistic yet and there's no way you can sit on +3 advisors across the board, so a proportionately larger amount of your potential is reliant on ruler quality, and this is really nasty if you're in a non-western/eastern/ottoman group. For example in 1.7 Inca could finish westernizing in the late 1400's, where Maya or unlucky Aztec realistically couldn't until 1520+. This has large ramifications on catch up rate, rate at which one can actually get +3 advisors, and so forth.
You also have some diminishing return. It isn't super strong diminishing return, but the difference between a 3/3/3 and a 6/6/6 is not as punishing as that of a 3/3/3 and 0/0/0. Finally, you have the utter horsecrap that is regency councils; getting one of those in the first 10-15 years can easily be ruinous if it's long.
The designers put in republics for players who want more agency over their monarch points. However, they missed the point in that they made the requirements for becoming one
1. Gimp you in the early game (you have to stay small-ish until you complete 2 groups, which can be a very long time if you're not western and pretty long even if you are in some cases).
2. Rely entirely on random luck to avoid a luck dependent government (IE the weak claim/no heir thing).
In 1.6, the patch notes said that noble rebels would force you into a republic, and that was true in 1.6 and 1.7. Then in 1.8 this was removed, but suddenly they decided that this was no longer worth mentioning, despite that it was an important part of your choices during westernization (take a hit to 50 RT and pay out big money in a tough period...well at least it was tough in 1.7...or stay as a monarchy and fight the rebels/westernize slower).
This puts us back at 1.5 crap. Jump through hoops and hope you get lucky in order to avoid having to get lucky (derp), or just sit on the luckbox monarchies all game long. The most annoying part of the whole nonsense is that by the time you can willingly switch into a republic (without the luck of revolutionary rebels which still flip you, but may or may not ever touch your capitol to do so), the negative impact of poor ruler luck is diminished and in most cases you were either screwed or not screwed already.
Monarch points and player agency in them is off kilter and remains bad design, even if the pay-wall NF feature helps it to a degree.