They certainly exist separate of each other. That we all have to call into question the timelines is half the fun.
Concerning times they exceeded warp 10 in TOS:
- "By Any Other Name" - ROJAN: And we'll go faster yet. Increase speed to warp eleven.
- "The Changeling" - ENGINEER: It just won't stop, Mister Scott. Warp eleven!
The narrative awareness and scaling has changed over time. I imagine largely due to people like us.
This isn't concerning streaming availability, but rather poor executive decision-making that deprived us of potential glory!
Edit: the discommendation gif is directed at Paramount, not you