Why qiyaam ul layl done with jamaat in Masjid not permitted?

Only Farzs and Tarawihs salaahs are reported to be performed in jama`ah in Masjids. None other salaahs can be tolerated to take same envergure without concrete sunnah practice. As such tahajud as defined qiyamullail can only be prayed at home and individually as described by hazrat Aisha (r.a.).