Correct, and that RAW is a data point that I'm ultimately using to support my ruling.
That's true, but again, the RAW is that the spell lasts for its duration unless otherwise stated. That is another data point that ultimately I'm using to support my ruling.
For the record, I'm not going against the extinguish line. I'm ruling that tidal wave extinguishes the flames and then they reappear immediately. That would satisfy both the Tidal Wave clause and the Wall of Fire duration by RAW. It wouldn't be particularly helpful for those folks who want Tidal Wave to defeat Wall of Fire of course.