I can't really support the argument - too random. If you're a good player you'll thrive despite the bad circumstances. Not to mention the fact that now the player has more control over the point distribution through national focus. As for its abstractness: it is a game, rather than a simulator.
Your argument is a standard cookie-cutter one with the standard flaw. Noise factors against skill don't make the influence of skill greater, they reduce it. Take a theoretical situation of two players playing 100% identical ability with equal starts. One gets a 5/5/6, other a 2/1/0, early in the game. It's extremely unlikely that the latter will ever catch the former, despite equal play ability.
If skill is relatively equal, bad luck in this regard can overpower it and result in one side winning not because of his ability, but rather because he got lucky even though his opponent outplayed him. Ruler stats are the perfect example of bad RNG design: you get a large (potentially game-altering) impact from a relatively small number of rolls, such that extreme cases can decide the outcome.
Early game rushes in civ IV shared this problem. As the game wore on, skill between players would allow expansion and tech rate to differentiate, and collateral plus larger armies mitigated the importance of any single dice roll to the point where you'd have a better chance of being hit by a meteor while playing than to lose enough consecutive 99.9% odds for it to make a difference. However, early in the game, 3 losses at 70% odds is more plausible to happen, and could cause you to lose outright. As a result, a markedly inferior player could opt to just rush in hopes of an improbable (but given the skill gap, still favorable-odds) outcome and a game that carried heavy strategic depth could be reduced to a series of 8-15 dice outcomes. To claim that someone who got lucky on an attack and won at unfavorable odds (IE made a stupid attack and got lucky) outplayed the other or that the other should have overcome his luck with skill in such a scenario is patently absurd and frankly insults the one who lost.
Monarch points from rulers aren't as extreme as an early civ IV rush, but they're cut from the same cloth. Unlike quite a few things in the game that are also random (even stuff like combat dice), they lack significant player influence/choice, but have a large impact on a low #checks. Just as importantly, had the game been shipped with monarch stats having less variance and more being dumped into base gain for all nations, I sincerely doubt anybody would have flinched as a player, considering it was a new model regardless.
Power projection (though wonky right now that pirate bay > conquering rivals by a wide margin), ROTW changes, and national focus have helped to improve player agency here, it's still a sore point in the game albeit less than before.
Personally, I think Monarch Points are a fantastic system and I enjoy the randomness because it adds a sense of difference between different games / different times in the game, while providing enough control to get through the rough spots. I don't really enjoy playing Republics because I can always optimize my Monarch Points with them, and don't feel as though I have to adapt to circumstances. However, people aren't *wrong* for preferring predictability over randomness... they just have different preferences in games.
The most vexing thing about republics is the combination of low variety of starts that have them (and all but 1 are in Europe, unless you count tribal governments which don't share the control aspect) and reliance on luck to get into a government type that isn't dependent as much on luck

.