This is a good point! And very possibly a plothole in the story, because it really would have made more sense for him to bring the Jotnar in secretly if he wanted it to seem like an outside assassination attempt. On the other hand, he's also in the middle of a mental and emotional breakdown, so cold logic is unlikely to be the main motivating force of his plans. (But on a meta level I strongly suspect they had the Jotnar come across the Bifrost mainly because they wanted Loki to freeze Heimdall.)

Frigga as a traitor would be....really interesting. Frigga + Loki in court intrigue against Odin = do want!