As anyone who clicked on this question is probably aware, shots and shooters have a tendency to make people lose control. Many cocktail bars in Tokyo pride themselves on their relaxed atmospheres, enabling customers to have a few lazy drinks before calling it a night. That's clearly not the environment where bartenders would want people becoming loud and annoying because they put back too much tequila. Certainly there are plenty of places with completely different atmospheres, where they are happy to serve you as many shots as you like. If you must have shots, drink them there instead!
I’m Whiskey Richard, and I am the founder of nomunication.jp. I’ve lived in Tokyo for over a decade, and I am a certified Shochu Kikisake-shi/Shochu Sommelier (焼酎唎酒師), Cocktail Professor (カクテル検定１級), and I hold Whisky Kentei Level 3 (ウイスキー検定３級). Click here for more details about me and this site. Kampai!