That's a misinterpretation of the Queen. The Queen IS the Borg. The collective is self conscious. It's a giant brain. And the Queen is the result of that brain.
The Queen is not the leader of a Borg hive mind. She is the collective mind.
"The Borg" is/are a single individual represented by a female. And that individual was lonely. And Picard was amazing enough that she wanted him to be a special drone with individuality so she wouldn't be alone anymore.
Which would be a contradiction of what Hugh says in I, Borg. He talks about the voices (plural) of his brethren that he hears. They are not centered or centralized. They are collected. Indeed, that is in essence what was observed in previous episodes, that the strength of the borg was in not having any sort of centralization.