The issue is entirely with the wording and how that affects the timing. Extinguish specifically says that it happens during the roll dice step, before damage and effects are applied. Freeze says that it happens after an object has both Freeze and Burn conditions on it.
Regarding intent, I wish I could give more insight here. Feels like I should be able to since I was part of the team to design the condition, lol. But between there being so much time since the condition was discussed, and the fact that final design is still the sole discretion of Arcane Wonders (so I can't just say how I think it should work and confuse you guys thinking that's for sure how it should), I'm not certain what the final intent was.
If we did want it to behave like you guys are suggesting, it would need to say something along the lines of "If (this condition) would ever be applied to an object with (other condition) on it, remove that many of (other condition) instead of applying (this condition)." The point being that it needs to say the removal happens before / instead of the application of the new condition.