You can max persuasion and still fail some dialogue checks because its against an attribute you have little or no points in. Some checks just have absurdly high requirements.
Most of the time, persuasion is about giving dialogue a different flavour even if the material outcome doesn't change much. There are numerous persuasion checks which seem to avoid combat but if you pass them, it ends in a fight anyway. The dialogue is different though and sometimes it feels good to have different conversation options appropriate for several varieties of silver tongued trickster.
While avoiding spoilers, there is one story event where persuasion is important on your main character and can have a profound impact going forward.
You can respec at any time from Act 2 onwards, so you shouldn't feel like you are misallocating civic points. If you are repeatedly failing conversation checks, put on some +persuasion items or use the respec mirror then try again. See if the outcome changes or if the conversation turns on it.
