Such statements seem to deliver praise and criticism.
When people say "She's hopelessly {adjective}", they mean the trait the adjective refers to is so ingrained in her personality that there's no saving her from herself—there is no hope she could ever be turned into the opposite kind of person, and to some extent, that is a good thing about her.
She is hopelessly romantic means she can be counted on to make impractical choices but she has a good heart.
He is hopelessly dull means he can be counted on never to say or do anything interesting but he has no real vices.
Timely progress updates from a business associate are usually things to be appreciated. But if the speaker prefers a more leisurely pace—he may always have many tasks to accomplish and thus a need to pace himself—too much quickness on the part of an associate can be an unwanted trait.
He is hopelessly quick may therefore mean that he can be counted on not to slack off and delay things as he always puts in a good effort, though he may not know when to give his colleagues a respite from the relentless tasks confronting them.