The only reason why you want to build dynamically linked binaries is to reduce their size, but it's pointless for bitcoin since you have to download 30 or so gb blockchain data, so why not ship it with a bundle of all libraries used and statically link them, the binary file will be bigger by couple of megabytes but I don't see it as a big deal. And this will prevent issues such as this as well as prevent attacks from 3rd party developers who willingly or unwillingly introduce vulnerabilities in the bitcoin core via updates.
IMHO bitcoin core should maintain it's own SSL library to avoid such issues in the future, in fact it shouldn't rely on 3rd party, regardless if they're open source or not dynamically linked libraries to avoid any possible attacks too.
In software development, it's generally considered unwise to reinvent something that already exists in an established and scrutinized form.
LibreSSL isn't reinventing the wheel, but rather repairing a broken wheen, and as LibreSSL grows more mature, and since it's a drop-in replacement for OpenSSL, it will with time deprecate OpenSSL and I'm sure the Bitcoin devs are wise enough to make the switch at some point.
