Fey Light in FCoB

[alsims2007]

If you have 940 TP or less every 3 seconds for the entire fight, you will get the same amount of TP regeneration for the same amount of time, period.

If you get to the point where you can use Invigorate without wasting any TP 10 seconds faster, then that's 10 seconds each successive Invigorate happens, and 10 seconds you're more likely to get an extra one in, or burn up the TP from it before the end of the fight.

Also, skill speed affects speed of autoattacks, which are 25-30% of your damage.

(sigh) exactly. Same in the same time. But the point of increased speed is that you do more skills faster, more damage should mean you kill the boss faster but tp doesn't naturally recover faster. So less ticks, less tp when you reach 0 tp. Paeon/goad is needed or sit there waiting negating the effects (the extra damage) overall for the entire boss fight (has to be a boss fight cause that's the only time tp really plays a factor)
Technically speaking if you finish a fight at the same time with boosted Ss what benefit did you get? None, you finished at the same time, you didn't finish any faster.

And ss does not affect autoattacks. Attack speed does (grease lightning and huton)

Oh wait are you thinking increased skill speed affects invigorate? It doesn't, skill speed only affects global cooldowns, not off global. You can view your action's recasts and test for yourself.