I realized that considering merely an upper limit for speed per se can hint at gravity(more precisely black holes).
Very naively with Newtonian mechanics, one can derive the following formula for escape speed from an object with the mass of $M$:
where $R$ is the radius of the object and $G$ is Newton's gravitational constant.
If one sets an upper limit for speed then the upper limit for escape speed for any object is also subject to the same limit:
Then one can see that it surprisingly gives the Schwarzschild radius, which is somehow correct because even light can not escape black holes!
So this way one can predict black holes and their size using merely Special Relativity. Does this signal a deeper connection or it's merely a coincidence?
I know that one must use full SR to derive the correct relation for escape speed but still doesn't reject the spirit of the idea.