This is why you're one of the better pro-Templar posters on the forums. 
Hey displayname? Take notes from MisterJB if you're pro-Templar. Despite our differences in views, JB's got a decent head on his shoulders.
Thank you. That's really flattering.
To elaborate on the idea, imagine if; rather than standing outside with an army of Templars, imagining how the mages were agreeing to commit unspeakable horrors; Lambert had been in the conclave, along with other Knight Commanders like Gregoir.
The obvious benefit is that he would be separated from his troops and the voice of moderate Templars would ensure the needs of non-mages are not forgotten amidst Adrian's hysteric shrieks about injustices and it would remind the mages that secession does mean war and that it might be better to reconsider it.
Granting them the right to vote would have avoided the war outright since the mages were never of a mind on it and, afterwards, Templars like Gregoir could vote against others like Lambert when the subject was the level of freedoms to be granted to mages.