Thrashing is why
Sorry what do you mean by 'thrashing' in this context?
Reload causes skew causes reload
How does reload cause skew? Reload will just load the latest version of the webapp. That's the point.
If you force a reload before the rollout is complete, the user will still experience skew, because you haven't finished the rollout. The website will be completely unusable for a significant fraction of users. You might as well turn off the website during the rollout. This is the main concern of skew - how to keep the website usable at all times for all users across versions.
If your rollout times are very short then skew is not a big concern for you, because it will impact very few users. If it lasts hours, then you have to solve it.
After the rollout is complete, then reload is fine. It's a bit user hostile but they will reload into a usable state.
If a webapp rollout lasts hours, you have a much bigger problem than skew which needs to be addressed urgently.
For most large scale apps (web or native) rollouts take multiple hours or even days. Ramps are slow to avoid widespread incidents and allow canary analysis to detect issues.