Celebi has bad typing, as well as a limited movepool. Jirachi just has a limited move pool.
Suicune, Entei, Raikou?
Suicune is just a bulky water. Not sure about the rest.
Heatran, Regigigas, Cresselia, Phione?
Regigigas has a poor ability, and due to the abundance of Fighting moves, would be easily (even though Legendary) ko'd. Phione lacks Manaphy's Tail Glow, it cannot increase it's Special Attack easily, therefore is not banned. Poor stats as well (I think). Cresselia has a limited movepool I believe, I'm not sure about Heatran though.
Uxie, Mesprit, Azelf?
Limited move pool, as well as semi-poor stats. They each only have two decent stats, everything else is meh.