(just gonna post this on this page instead)
I read in reddit that in Japan this works like that: everytime you spend mythril on a banner and you get no 5*, there is like a hidden counter that makes the probability to get a 5* in the next pull higher. I don't know if it works for global like that, too. I highly doubt it.
As far as we can tell, no.
As for the FFT banner, I've come to the conclusion that a lot of people were pulling under mistaken assumptions that the 2% rates on certain lower-tier items applied to the FFT banner. Those rates (which in Japan are available thanks to law) only apply to 7-item banners, e.g. the events that have two banners.
FFT is a single 9-item banner. Those rates don't apply. While we don't have a barometer for equivalents just yet with the new 13% rate as far as events go (all other events subsequent to the change to 13% have been 2-banner ordeals) it's closer to the SSBFest banners than a regular 7-item event banner.
Certain parts of reddit very well knew this already. If you check
this document which reddit posted ~a month ago, those assumptions on the bottom chart are based on a 1% pull rate.
So what we have right now is a bizarre overlap of several factors - Global's typical look-ahead-and-overhype-certain-banners factor, which is afforded since we know exactly what JP got at any point in the timeline, leading to hoarded Mythril and perhaps a slightly-higher-than-factual perceived value of a few relics, crossed with simple misinformation on chances, which is leading to massive amounts of otherwise undue salt, along the lines of 'why did DeNA nerf the banner? Do they hate Global?', which as far as I understand is an incorrect statement based on the evidence above.
As to streaks, yes, they happen. On Global, historically it's led to a lot more fallout just because of the aforementioned hoard-everything-and-blow mentality. It really, really sucks when your savings for a few months results in zero of the items you want.
I'd go out on a limb and say this problem barely exists in JP, because you don't know what's coming next. You don't know if your current awesome banner is a local maximum for some time, or if the next banner over is going to be even better. You don't know when the orbfests are. You don't know when a double BSSB event is going to hit. So you just maintain a stockpile of Mythril you think is sufficient, especially for Fests, then pull when the banner looks good, all without the fuss of 'okay, well, I'll plan to have 300 for _____' and ending up with nothing. And guess what?
F2P players exist on Japan and are thriving with a very reasonable success rate without all that planning ahead to whale 500 Mythril on a select few banners.
DeNA isn't obliged to change anything with regards to how pulls work. If people start quitting, maybe something will happen since they -are- a business and one that relies on retention and monetization, but other than that, they're not beholden to easing the pain, so it were, for people (well, the majority, considering we all want to min-max a limited resource, that being Mythril) who want to play this game a certain way, planning ahead and dumping into certain banners. It's also not a concept completely alien to them considering the Beginner banner literally is set up that way - you get a courtesy 5* regardless of your luck. So if they're not doing anything past that, then they simply aren't.
p.s. bears repeating that I know what it's like - first 6 months of the game I had two character relics and 2 5* armor. Went 1/44 on the first lucky draw, currently 1/34 on FFT banner. And again, along with every time I repeat this I fully acknowledge that the way I play this game, with my massive grindfest stretches, isn't exactly a good barometer to begin with.
edit:
p.p.s. and yes, getting completely sick of gacha and quitting (for greener pastures as far as games go, or swearing off gacha mobage altogether) is a completely valid response, because in the end, if you get shafted, you get shafted. Not saying you should suck it up, and ESPECIALLY not saying you should cave in and start whaling.
p.p.p.s. I had half this post already ready before FFT because I suspected we'd be at this point of the cycle ;p