The evidence points elsewhere. TLS is such a complex protocol that any new library will make fundamental errors in implementing it and the requisite crypto primitives (of which there are many).

What crypto libraries need is usage and, this usually goes with it, attention from people looking to break them. There are plenty of TLS libraries out there like mbedTLS and the mentioned JSEE, and looking at CVE reports a few years ago you would think these are the most secure libraries in the entire world compared to the constant trickle of issues in OpenSSL. Except when heartbleed got attention and people started looking at these rarely used alternatives they found massive problems. For years, the protocol FSM in JSEE was fatally broken. MbedTLS had and continues to have issues with just basic things like buffer overflows. And often these libraries just plain lack features and timely updates.