In your original post, I took
> Only if you know them. ... You can't log into the website without that account key.
To mean that you'd openly have access to information in front of the guard, and then let them know that you can't access it at this time because of your elaborate scheme (e.g. tell them that it exists, but that they can't have it).
That's quite different to just not travelling with the data (or evidence of it existing) at all.
> CBP isn't the only reason to want to have Travel Mode
No, but it's the only 'reason' that's likely to use serious, life-altering coercion to make you to disable it, if they detect that it exists. It may be better to have no data that suggests capabilities, than openly posses partially disabled capabilities.
There's no way for a border agent to tell if you're refusing to disable travel mode because you won't or you can't (and little reason for them to care).