It doesn't have to be liked or agreed upon. Options are always good and thinking that way, for every YES on devs perspective they should create a NO. So for every design initiative they should create an option. It already exists and is called Android.
However, if the conversations are that private, I won't leave my freaking phone away from me. I keep it closer than my shirt. Why? Because I know I am dealing with private stuff, so I don't want to show off my phone till I'm done with it.
But again, that's not a solution.
Answer to OP- there is no fix. It is what MSFT has chosen by design. Glance and Go. You look at 5 words preview or name of who sent, if you want to open it, you bother taping and sliding. If not, you put your phone back.