There is no way Michael could've let Tattaglia live. The Tattaglias not only killed Luca, but they had Carlo set up Sonny. Even though it was Barzini who approached Carlo, the killing was in retribution for the Tattaglia son. So Michael had to kill him to avenge his brother's death.

As for the the other two, why not? Obviously they had given tacit approval for Barzini and Tattaglia to wage war against the Corleones. If you remember, Barzini broke the peace several times while Michael was taking over the reins from his father (and it was Michael's inaction against them that made Tessio turn). I would imagine that was part of the reason that made Michael want to wipe them all out.