re: What’s a great net worth by 45?

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You have to answer the question, what is a pension worth?

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So, using my example above, if you figure out how much money I'd have to have in the bank with a year in and year out average for that investment (probably 1.5% / yr) and treat the $5200 / month as a dividend, the amount needed to provide that would be about $4.16 M.

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This estimation is pretty far off from reality and you are grossly overestimating the value of the pension. It would be more accurate to say the pension is worth $1.56M and even that is likely an overestimation (although this can't be accurately known until after the fact at which point who cares because you are dead anyways).

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you can never touch the principal

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You cannot because you have no principal really. When the benefit ends there is no principal left. It is more accurate to say you are actually completely depleting the principal down to $0 at the exact moment you die.

The big benefit of the pension is the lack of volatility and relatively known outcome. The other scenario where you are using retirement (IRA, 401k, etc.) and other investment accounts has a much larger spread of outcomes. A more accurate representation would be using the "4% rule" and assuming your yearly benefit is equal to 4% of the starting balance and then adjusted up for inflation (thus 25x your annual benefit for estimating the value). If you have no COLA in the pension then it is actually even lower than 25x.

One thing most people don't discuss are the wide possibility of outcomes. There is even a lot of discussion regarding the 4% rule being too high but in reality it may be too high for the worst case scenario but is actually too low for the vast majority of outcomes. The trinity study and the updated studies after showed that using 4% of the starting balance and then adjusting for inflation yielded like a 96% success rate (did not run out of money). The median case was that the ending balance was almost 3x your initial balance and the best case was like 12x the initial balance (maybe more I forgot the exact number).

Of course in the non-pension portfolio if you experience the worst case then estimating the pension worth based on 25x the annual benefit is an under estimation of the value. If you experience the median case meaning after 30 or so years the balance actually grew to 3x the initial balance even after you withdraw 4% per year and increased it with inflation. In that scenario then 25x is a large over estimation of value. In the best case scenario where your balance after 30 years is 12x the starting balance then the pension value is actually quite miniscule.

The whole point is that even using 25x the pension is still extremely likely to be an over estimation of the pension value but probably a fair assessment based on the general rule of thumbs. This also doesn't even take into account the probability the pension fund dissolves and you lose your benefit. For a government pension that is extremely unlikely but for a corporate pension it sure isn't 0%. You would likely want to discount the pension value based on some factor based on the health of the pension plan and probability of losing or lessened benefits in the future.

What is also missing is for people who do not qualify for SS due to their pension. We typically don't calculate our SS value in net worth. So if you are comparing 2 scenarios and using 25x your pension benefit (and don't get SS) and in the other scenario you value your SS benefit at $0, then you are likely way over estimating the pension scenario comparatively.

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You can never touch the principal, but that is the goal with a retirement nest egg as you hopefully can take distributions without touching the principal, or if you do, hoping it outlast you.

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I don't know why the goal is to never touch the principal. That is absolutely not the goal for most people. The goal is to not run out of money and to live the life you want to live. Some people may not want to touch the principal but unless your whole goal is to make sure your heirs receive a large inheritance that should not be your goal.