People seem to have repeatedly gotten hung up on the need to incentivise miners to lengthen the braid/chain, instead of widen it.  This isn't a need: miners will contribute to the highest work braid/chain simply because that is the one most likely to have other people contribute to it.  No extra incentive is needed.  If there exist two childless beads (blocks), it's in my best interest to name them both as parents.  That generates a higher work braid.  Naming only one of them creates a lower work braid.

Note that Satoshi's analysis and the "longest chain" rule is simplistic and only works for constant difficulty blocks.  It is very straightforward to combine the work from multiple blocks even having different targets and evaluate the total amount of work.  It's not equivalent to the chain "length" but the calculation is straightforward.  I leave it as an exercise for the reader.  ;-)

Note also that my work is entirely based on proof-of-work.  I don't think proof-of-stake works and you can't apply a profit maximizing rule to a set of numbers in your computer that fundamentally have zero marginal cost.  (For more on proof of stake, read my blog: https://blog.sldx.com/whats-wrong-with-proof-of-stake-77d4f370be15)