Bootstrap isn't the source of monotonous websites. It just makes them look better.
Source of bad design? No. Source of bad taste? No. Source of monotony? Yes, just out of convenience.
Why should every web application look different?
If it was up to me, the browser default styles would be something closer to Bootstrap (and actually implement stuff like the <menu> element), so you can build a decent looking site with touching CSS at all.
That's a remnant of the past and it's changing quickly. Look at any consumer app developed and released in the past year. Most have custom elements, layouts, etc. The web just did it first and is further along in the "designification."
Native apps all looked the same because they were all designed, built, and used by largely engineers. As computing (both usage and development) becomes less esoteric and more powerful, design will naturally become more expressive and purpose-built. This trend extends back to DOS as well and applies well outside of computing (cars, buildings, clothing, hardware, etc).