I think it is accurate to a point. Without trying to break the game...I think the conclusions are ABSOLUTELY correct.
Due to the effects of bounded accuracy and purposefully limiting how well one can hit against a creature, the amount of damage you do is probably the most important factor in KILLING (as opposed to other tactics of getting past like talking to it) monsters in 5e.
However, the difference between a Fighter that hits with a +11 - +14 against an AC of 21 will hit probably most of the time or 2/3 of the time. If they deal 20 points of damage and have 5 attacks per round after three rounds they should have done around 200 points of damage. Not bad.
A Fighter that hits with a +20- +21 (+6 Prof, +9 STR, +3 Magic, +2 Bless or Proficiency Die somehow) will hit 100% of the time. If they do 15 points of damage a round they will do 225 points of damage per round.
So, in this scenario, MORE damage is pretty important, but even if they do less damage per hit, because they hit more often, they end up doing MORE damage.
I would say the Damage and to Hit are directly proportional in 5e.
For the above scenario to balance out the Second Fighter would need to do 2/3 the damage of the First fighter (so around 13 Damage per round gets it close)...as that is proportional to the 2/3 to hit that the First fighter has. In that light, damage and to hit % might be directly proportional in how much they affect combat and taking down enemies.
For those who go out of their way to try to boost their To Hit or AC to the point that they will try to break the game if they can, I think the To Hit and AC start gaining prominence.
As such, in these instances, the To Hit or ability to hit a monster, from what I've seen is directly proportional to damage in relation to how effective it may be (at least to a point, # of attacks is ALSO highly important).