This is very interesting to me, thanks for writing it up!
Together with a couple of other Holy Paladins I've been responsible for a fair portion of the recommended gearing strategy for Holy Paladins, most notably in the Paladin Discord (Hammer of Wrath). I maintain a big spreadsheet that attempts to calculate stat weights and do trinket recommendations, and I built WoWAnalyzer.com (and its Holy Paladin implementation) to assess actual performance of talents, traits, mastery and items from logs to provide data to base recommendations on. Long story short; I know a thing or two about Holy Paladins and the recommended gearing strategies.
A best legendary does competitive HPS compared to alternatives, is reliable, not much harder to use than alternatives and helps save lives. A top parsing holy paladin is often one that underheals a fight. It's still very important to play very well to get an absolute top rank (which a lot of people consider to be the best), and hitting the right buttons at the right time and often enough is way more important than the legendaries you pick. I'm pretty sure you can get just as easily get a top rank with any combination of the the top 5 or 6 legendaries.
I believe a Krosus-like fight is a pretty unique fight that you don't see a lot, but it's definitely a nice start. Warcraft Logs statistics seem to give some different results, but I guess that's not "personalized"; https://www.warcraftlogs.com/statistics/11/#class=Paladin&spec=Holy&combatantinfo=Legendaries&metric=hps®ion=1
Are you considering the damage taken from Light of the Martyr in your simulation? From my quick calculations I reckon they'd end up at basically the same HPS (±2k) if you adjust the healing done by that as is done by all acceptable loggers and models. Also I'm seeing that you're using the old 4 set with very low critical strike chance (for that set), when you'd run a more acceptable critical strike chance you'd find that you're proccing the 4 set bonus more often which would make the opportunity cost of casting a Maraad's boosted Light of the Martyr worse. It's also unclear how well this sim was at using Velen's and Ilterendi, if you don't do anything special they'll perform slightly worse. Is there any form of mana insight? Mana is very important.
I'm left wondering what the point of showing these results was? It doesn't show us that it's right and that OP should continue to rely upon Mr. Robot, it just shows the results he was apparently already aware of, with questions whether it's actually accurate still remaining.
This is true for a large part, but keep in mind that a large part of these trends are started by people that have done their research and did base it on real data. Still our recommendations are based around more than just data showing their HPS throughput. One such additional factor is "utility"; legendaries more likely to save lives where it matters (e.g. Maraad's Dying Breath) get valued a little bit higher than legendaries that provide passive but often insignificant healing (e.g. Obsidian Stone Spaulders). This is a heavily discussed subject, so we try to only make small adjustments. There are a few other factors we take into account. This is also true for our other recommendations, like trinkets (for example Deceiver's Grand Design can be responsible for a lot of HPS but it's generally valued weaker).
We don't believe that healers should be 100% focused on HPS but instead on killing bosses by keeping people alive. Losing a small amount of HPS but gaining life saving capabilities (such as with more spot healing, damage reductions, etc) is often a positive exchange towards killing bosses. The lost HPS is often made up for with reduced overhealing from yourself or from other healers, less damage taken or elsewhere.
Directly healing tanks is considered inefficient and only done if needed to keep a tank alive. While healing melee while standing near melee is preferred, it can not be done exclusively as this would simply cause too much overhealing. We try to spot heal whoever is lowest, and while our Mastery is important we do not hesitate to heal low ranged simply for the fact that keeping everyone alive is far more important than maximum mastery effectiveness.
No, we do not. I have never heard of anyone overhealing on purpose, and quality healing teams are working together, not aggressively competitively against each other. This means actively trying to avoid sniping other healers in your team. One small exception is that the general recommendation during the Velen's buff is to use the highest efficiency spells even if you expect it will overheal since Velen's will work nicely with that, but your goal is still to avoid overhealing as you'd still lose 50% healing when you do.
I'm excited about this. Having another source with a considerably different approach to base our theorycrafting on can be great. If the simulation is accurate enough this could even beat our log analysis through WoWAnalyzer, and give insights into some of the harder/impossible to accurately measure effects such as Divine Purpose. Of course we still wouldn't base our recommendations on HPS alone, but we've always taken it into account significantly so it (presumably) being more accurate is going to be helpful for us too.
At the same time this sounds scary. Making recommendations purely on HPS throughput will misdirect people towards selfish and unreliable choices that in the end make their team weaker.
I have to admit if I had the time I'd be building a simulator to make stat weights to replace my spreadsheet model. When executed well it's definitely a better way to do it, but when we're unable to review the implementation it's hard to assess if it's done well and worth recommending to players wondering about their stat weights, trinkets, other items and legendaries.