No need.
Since my ESO account was a regular PC account before it was linked to Steam, I can play through the regular launcher.
I also have all the DLC/Chapters purchased for my ESO account, not through Steam. So I maintain access no matter which launcher I use.
Finally, I sub through ZOS, not through Steam. That way I keep access to my sub when Steam goes down.
I basically only play through Steam for social reasons, but it's no sweat off me when it goes down.
If I didn't lose my progress or anything and didn't have to rebuy anything... very much YES! I would unlink it. I don't entirely blame Steam for the issue, if their servers failed to verify your login, you wouldn't see a time out error, it would be a different error. I'd more point my finger more toward Zenimax on that part. However, there is a clear issue between the servers working/communicating with each other it seems, and if that could be avoided, be it whoever's fault, then yes I would gladly do so.