I don't know this firsthand, but I've heard from many people that had delved into OpenSSL code that it is an example of code where "many things could be made better", to put it lightly.
Only after massive security vulnerabilties and a lot of media attention more people looked at OpenSSL in detail and eventually decided to do something about it. Which mostly was "let's write a new library or fork it". Thus, LibreSSL, sodium, nacl and such.
What got us in the mess with OpenSSL, was to leave a key component of many software projects to a struggling, small team. It's amazing how much open source relies on a few ancient programs written and maintained by few with little to no financial support (e.g. NTP, GPG).
Right, but those vulnerabilities _were_ found. I worry that they wouldn't be found in this. The only people who'd go looking are the people who see that a specific website is using it and want to exploit it.