What makes it bad is when you get situations where the player couldn't reasonably account for them. There's not a whole lot you can do differently in most cases; you simply do less of what you'd do otherwise. Whether we introduce more control or not, it would be better if the player interaction with this mechanic carried more strategy.
As for "unavoidable catastrophic failure", monarchies/monarch points make them happen needlessly frequently by putting such large weight in terms of gameplay on so few rolls. There's a reason you see me complain about this, but not about the combat dice. The latter are every bit as "random" in that they use the same logic (AFAIK) for getting numbers via RNG as monarch stats or death timing. You can't control those dice either, but you can make choices that push you in greatly in the winning or losing direction regardless. Lots of choices, in fact.
For monarchies and their contribution to your resource pool, it's a lot more limited and a lot more dependent on what the game happens to decide you get. There are some cases where this might impact your decision making, but in most cases this fraction of the resource operates largely independently from player input and it's hard to see what it adds to the experience.
If you want to say that regency is worse because it actually locks out large portions of the gameplay however, I'd be inclined to agree.
Edit:
I guess we would need to define "catastrophic failure" though. It's more just an issue of progress being set by the game rather than the player once you get to the low ends of the distribution, whereas in most areas of it a majority of players will find other constraints limiting them more in practice, even at below average-to-average point incomes.
To illustrate, you'd need to be a reasonably strong player to truly press a 6/6/6 ruler income to its limits in terms of extra coring progress, because you still have to come up with money, manpower, and favorable diplomacy. At 0/0/0, you're gimped sufficiently that your monarch points can easily bottleneck you. At 3/3/3, your potential is less than 6/6/6 but the difference in progress is nowhere near the jump you get going 0/0/0 to 3/3/3.
National focus helped a lot since you can smooth the distribution in terms of which monarch point gets more or less, but very low values are still rate-screws regardless. I can understand that from a risk/reward standpoint since on average, a monarchy will be stronger than a republic in point incomes, but I dislike the inability for the game to let you hedge your risk in the vast majority of positions during the very time it matters the most.
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