The point of travel mode isn't to dodge border control policies or questioning; the point is to prevent the exposure of credentials when travelling, even if the exposure is to a border agency.
If a border agent asks you directly, "Did you remove information from this device to prevent us or others from seeing it when entering or within this country?" the only truthful answer is "Yes", but travel mode has still achieved its goal. Even if they confiscate your device, they can't access the credentials. You may have other issues entering the country but your data is kept secure and private.
At some point, you're going to have to have a separate device for international travel. Then they'd have to ask: "Do you have another device back home that you didn't bring because it contains sensitive information?"
Even back in the 90s, I knew people who would bring a separate travel laptop that would just have the basic set of apps and a VPN client. So, once you got to your destination, you'd login via VPN and download what you needed. This was at Nortel, so it's not like it was a very high security company, just moderately secure. Not everybody did that, but certainly enough people did. The department kept a couple spare laptops for just this purpose that would get wiped and restored to their default config after the travel.
If a border agent asks you directly, "Did you remove information from this device to prevent us or others from seeing it when entering or within this country?" the only truthful answer is "Yes", but travel mode has still achieved its goal. Even if they confiscate your device, they can't access the credentials. You may have other issues entering the country but your data is kept secure and private.