Actually, this is NOT true.
Most breakthroughs and new ideas are based on the impetus
of either a logical inconsistencies of an established understanding (eg: non-covariant of Maxwell equation under galilean transformation), or based on empirical observation that simply violates current theories or has no explanation (eg: high Tc superconductors). Only THEN would one needs to come up with new physics to describe these things. One just doesn't start with thinking "outside the box" for no apparent reason!
This is a clear example of the faulty application of velocity addition in Special Relativity. Before you proceed any further, please do some homework on why the galilean velocity addition that you've used isn't valid for speeds approaching c. This is basic Special Relativity 101. This is not "thinking outside the box". This is not knowing what's in the box.