If there exists a fast factoring algorithm that breaks RSA, then investing in research to discover that would allow us to design and switch to better cryptosystems. If there does not exist one, discovering that fact would allow us to prove security guarantees about RSA; either way, we improve security.
If we avoid such research out of fear that we might discover something that breaks RSA, we are relying on security by obscurity.
Nobody is 'avoiding' that research. People already know a fast quantum algorithm exists for the factorization problem, which is the core of RSA. hence, people are already working on cryptosystems more computationally complex than RSA. Hell, even more computationally intensive than what quantum computers are thought to be able to do. The class of algorithms called lattice based cryptography are known to be impossible for quantum computers to break, even though these are fully classical methods of cryptography.
If we avoid such research out of fear that we might discover something that breaks RSA, we are relying on security by obscurity.