Question.Is it known/easy to see that every smooth projective variety $X$ (over an algebraically closed field), except for the point and $\mathbb{P}^1$, has a vector bundle which is not a direct sum of line bundles?

I have a result which trivially shows the above fact in positive characteristic, but I don't know whether I should state it as a corollary as it might be well-known or obvious for reasons I don't see.