White Gi was used by Takamatsu + Hatsumi during their training, because white gi is not really a trainning clothes, it was actually an underwear.
They use it because they dont want to make their clothes dirty
Thats why karate, judo etc that use white gi are not allowed (cmmiw) to use any shirt inside
Black Gi is use by farmer as their working suit. ninjutsu use black because ???
(think by your self

)
I wonder about this. Most ordinary traditional Japanese clothing would not stand up to more than 5 minutes of grappling (which is probably why Sumo is performed almost naked) but we have had grappling styles such as jujutsu for centuries, and not all armour based styles.
The shitagi worn under the keikogi of kendoka and iadoka is a very lightweight piece of clothing and would not stand up as a training jacket.
Remember that judo had been around for many decades when Takamatsu Sensei was teaching the young Hatsumi Sensei, and a dedicated gi was around by then as a general uniform for judo. But most judo or aikido jackets by today's standards would be far too thick and bulky to wear as underwear beneath kimono, yukata, samue happi/haori clothing.
I believe that training gi have existed for much longer than is commonly thought, but that they weren't as thick and reinforced as today's apparel, and that whilst some people probably did train in their underwear, sometimes an actual training gi is mistaken for underwear because it is more lightweight than what we are used to. I doubt if there was more than one type of keikogi and that karateka, aikidoka, judoka and jujutsu/ninpo practitioners all wore something like we see Takamatsu Sensei and Hatsumi Sensei wearing in those old photographs.
And today, we have people training in all sorts of gi colours, karateka in black gi, judo gi available in black (not that I know of an organisation that wears them), and we even have a few Bujinkan/BJJ cross trainers who wear white gi for taijutsu!
I agree that our black gi probably helped with marketing 'ninjutsu' in the 80s before we called it budo taijutsu or ninpo taijutsu, but I don't think many of us feel particularly ninjerish in our tatty old grey karategi. At least the more recent kit seems to hold its colour better! I now train in a black BJJ gi that is still black as jet and tough as carpet after a year and a half of training. It is hard on the nipples after a day's training, but at least I don't lose whole sleeves these days!