The cost is, if people start transitioning to a world where senders only transmit LF in opposition to current standards for protocols like HTTP/1.1 or SMTP (especially aggressively, e.g., by creating popular HTTP libraries without a CRLF option), then it will create the mental and procedural overhead of tracking which receivers accept LF alone vs. which still require CRLF. Switching established protocols is never free, even when there are definite benefits: see the Python 2-to-3 fiasco, caused by newer programs being incompatible with most older libraries.
2-to-3 fiasco was solely caused by inadequate support to write py2 compatible code until python 3.4. It was literally "you devs, stop write ugly py2, let's write godly py3".
