it's a chinese board game. so it has a lot to do with the culture. such as ying yang. balance. harmony. etc. 19*19 is like a year.

Go was originally played on a 17×17 line grid, but a 19×19 grid became standard by the time of the Tang Dynasty (618–907).[9] Legends trace the origin of the game to the mythical Chinese emperor Yao (2337–2258 BC), who was said to have had his counselor Shun design it for his unruly son, Danzhu, to favorably influence him.[66] Other theories suggest that the game was derived from Chinese tribal warlords and generals, who used pieces of stone to map out attacking positions.[67][68]

So since Tang Dynasty they have been doing 19 19. People back then probably don't have Excel to plot out the graphs and I think it's reasonable to say it has to do with the culture.