That's a very spesific case though. Nidhogg jumps at excatly 30 seconds into the fight. And as it turns out, 30 seconds is the sweet spot where with 824 SpS you get 12.96 casts in and with 850 you get 13.01. With 500 SpS you would get in 12.3 casts and that's pretty much as low as you can ever go with SpS. So at minimum you can do 12 casts and at maximum 13 before Nidhogg jumps if you're casting the entire time non-stop and start at exactly the right millisecond when the tank pulls.
Pre-casting before the pull affects this a bit in a difficult way. If you start to precast so that your first cast lands exactly at the same time when the tank pulls, then your second spell starts casting basically at 0 seconds into the fight, so while that gains you an extra cast, it doesn't change the amount of casts you can do in 30 seconds. With maximum SpS and a perfect pre-cast, you get in 14 casts total.
Now if you have a 1000 SpS, it takes you 29.29 seconds to cast 13 times. So with that you can afford to land your precast 0.7 seconds into the fight and still get the 14 casts in, but any later than that and you only get 13. So you need to time it with 0.7 seconds of precision to get that 14 with 1000 SpS, if you fail that 0.7 second window, you're either pulling early or getting only 13 casts in.
With 500 SpS, it takes you 29.25 seconds to cast 12 times so you need to work with almost the same precision if you want to get 13 casts in instead of 14. With more SpS you can widen the window and at 850 SpS you don't even need to precast at all the get 13 casts in.
So what you're saying is generally speaking technically a possible scenario and there are gaps like that in the game where spellspeed or skillspeed can give you an extra GCD usage, especially when you have a nicely contained scenario like fitting certain amount of GCDs inside a buff timer.
However your claim that it's SpS which gives you the edge to cast an extra spell before the jump is not plausible.
With 2.33s cast time you use 30.29 seconds to get in 13 casts, so that means there's no way you can do 14 casts and as long as you start precasting 0.3 seconds before the pull you can get 13 casts in, something you could easily do with a lot less SpS, technically even with 500 if you're very precise.
Instead what Taika claims that you can't notice the difference seems to be more believable. A more likely scenario is that you're actually losing some time in between those casts to something (healing and swapping targets, not precasting, latency, stacking instant abilities in between GCDs too slowly, potion lag or something else) and missing at least one possible cast entirely.
In any case you're talking about a 100 ms difference in cast time, which is probably a lot less than your latency. During those 13 casts that amounts up to 1.3 seconds spread over 13 tiny increments. What Taika said about the e-sports level precision is very accurate, I'm certain that some players are able to exploit that 100 ms difference, but any messy tab-targeting or lag or imperfect pre-cast and you've introduced a far greater noise to your rotation so I'm sorry for doubting your player abilities, but I'm fairly sure it's not the SpS which causes you to get that extra spell in sometimes. It's possible, but out of reach for the majority of players.
You're missing the point yourself.
Even if it is possible in certain scenarios to get extra casts in and certainly it's true for longer fights, it doesn't prove any point for or against. To gauge which stat is better you must understand that those points don't just go to waste, they go to CRIT, ACC and DET. It doesn't matter if you get 12 casts in instead of 13 but if those 12 are in total more powerful than the 13 weaker ones, then they're objectively better because of lower total MP cost. Especially regarding dps situations for healers, if your acc is below 100%, that means some of your precious casts are completely wasted time and MP. The sheer number of casts means nothing.
Also as to your other claim, in a 10 minute fight you can with 1000 SpS cast 266 spells if you do it nonstop, which never happens. For example in Nidhogg Ex, the very best (HPS) WHM according to fflogs has 188 ability usages during the fight which lasts 10 min 3 seconds. And that includes everything, including non-GCD abilities like swiftcast, virus and such. That's over a hundred casts less than you're claiming and that's an exceptional player.
Also with 500 SpS you get 246 casts and with 1000 SpS you get 266 casts in 10 minutes, non-stop. So that's 20 casts more if there are no pauses at all. So what you need to do is to gauge if you can gain more by investing crit, acc and DET for those 246 casts or is it better to cast more and weaker spells using more MP. Just saying there's more casts is ignorant. Also the benefit from SpS comes only if you cast a lot of spells with no stops in between at all due to movement or boss disappearing.
The only valid argument for SpS is that yes, it gives you that 100-150 ms faster GCDs which in theory give you a better reaction time but it's very difficult to exploit that and anyone claiming to be fast enough to do that is probably overestimating their abilities. Especially because almost everything can be anticipated so that if you actally need to rely on that reaction time and it's cutting that close, you're already doing something horribly wrong and should learn the fight a bit better.
In short, SpS is only better if the number of extra casts you can get with it (and you only get one of those extra casts if you are able to cast about 30 seconds straight with no breaks whatsoever) during a fight are in total more powerful than the fewer but more powerful casts you can get by investing the same number of points in other stats.