Seven is not given a Starfleet uniform because she is not Starfleet. She's not given a Starfleet rank because she had no Starfleet training. This is normal.
With the exception of the Maquis this is how Voyager handles all other non-Starfleet crew members such as Neelix and Kes. It's also consistent with how other non-Starfleet crew are handled in other series. The Maquis were a special case. Asking why the Maquis, and others, were given uniforms and ranks sheds light on why Seven, and others, were not.
On the Enterprise D Acting Ensign Wesley Crusher didn't get to wear a uniform. He was only granted this privilege after receiving a field promotion to Ensign. In Ménage à Troi he missed his transport to the Academy and Picard felt he should not wait any longer. (Thanks @Ghanima)
Janeway decided it was paramount that the two crews integrate to better live together on Voyager in the coming years. This was made easier because many were ex-Starfleet (Chakotay) or had some Starfleet training (B'Elanna). Janeway granted them provisional ranks which is why they have different insignia from regular Starfleet. They were given Starfleet uniforms, underwent Starfleet training, and were expected to act as Starfleet crew.
Tom Paris was pointed out by @Durakken in the comments. He's an ex-Starfleet, ex-Maquis criminal invited to Voyager by Janeway as a "Starfleet observer". Which appears to grant him the right to wear a uniform as he's wearing it before they head to the Delta Quadrant, but with no rank insignia. From the start Janeway is trying to bring Tom back into the fold. Upon losing their pilot, she reinstates Tom's former Starfleet rank of Lieutenant Junior Grade. Since he wasn't part of Chakotay's crew, and shows no attachment to the Maquis, he's treated as Starfleet to better integrate him into the crew.
What if Seven had rank? Now she's subordinate to people, people she might feel are inferior, something she does not deal well with. Worse, others would be subordinate to her; she is a terrible leader and would irritate those people. By leaving her outside the rank system Janeway cleverly reduces both problems: Seven only has the authority Janeway grants her, plus Seven's own personality, and anyone who has an issue with Seven can go to a senior officer to work it out.