As for Betazeds...the idea of an influx of Betazeds into Starfleet. Starfleet would have to rely on each one of them to police themselves and restrain themselves from accessing sensitive info for example. Starfleet would have to ensure they were all of good character. Any dodgy Betazed that slipped through the net would cause mayhem.
Betazeds really do challenge notions of privacy in the 24th century. It's difficult to see how anyone anyway committed to their own privacy could behave socially functionally around Betazeds.
The assumption being that the rest of the Federation share the same privacy practises as humankind? There are probably diverse issues of privacy in the Federation. I can see that Starfleet being an Earth based organisation of human origin does mainly have its practices set up to suit humanity with some flexibility for other species. But everyday living on other planets, more likely range from being as open as a Deltan to being as closemouthed as a Vulcan, with the Betazoids being somewhere in between.
If a being found it difficult to be around Betazoids then don't join Starfleet, don't get a job at Federation HQ and don't visit Betazed or any other telepathic planet.