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Seven wasn't allowed to join Starfleet, because she was a former Borg drone. But Starfleet had welcomed Picard back into the fold, despite the damage he had caused as the Borg drone Locutus?
We've covered this.
Picard was fully de-assimilated; he retained no Borg implants and has never referred to himself as Borg, which Seven emphatically did, usually at least once an episode. Even so, we see in episodes like TNG: "The Drumhead" and DS9: "Emissary", and arguably in Star Trek: First Contact, that there are people in Starfleet who do indeed hold Picard responsible, who resent him being able to resume his Starfleet career, and who believe him to be an "unstable element".
In addition, Picard already had a long established Starfleet career and was rehabilitated in the 2360s; by the late 2370s and early 2380s, after the Dominion War and around the time Voyager returned to the alpha quadrant, attitudes had started to change and the Federation was becoming more isolationist.
Lastly, let's not forget Icheb was able to join Starfleet, despite also being a former Borg drone (almost, nearly, kind of). Seven's attitude to being in something like a hierarchical command structure stank, as we saw many times in Voyager; and she gave zero indication that it was something she was remotely interested in until after Voyager returned to the alpha quadrant, even going as far as to on occasion indicate she wasn't particularly interested in returning at all. I daresay that for Picard, Icheb, and Seven, the Borg part of the equation was only part of the consideration. Seven continually banging on about being Borg and how that made her superior probably had more to do with it.