This is a nice feature, but ultimately if you are concerned with border agents requiring a phone search then you should just backup and install a fresh OS before traveling, then restore when you get back. Log into the minimal number of apps after you've entered the destination country, and optionally delete/logout of said apps prior to return travel if the return border crossing is also a concern. Admittedly if you use a password manager you might need still want to make use of a feature such as the one in this article, or install the password manager app after entering the country, or just write down the passwords that you will need and hide them somewhere unfindable with your stuff.

On iOS about the only thing you would lose is your message history during the trip. It might be an annoyance if you wanted to play games that had non-cloud-based saved player state, but I can't think of too many other issues with doing this.