Theres absolutely no reason why they can't do all of those things while still having Tierney. Also, White would get caved in playing that role. You cant have a guy who loses 53% of his faceoffs lining up in the defensive zone 60% of his time at ES and being your top PK C.
White is a winger. If you are really so intent on playing Brown and Norris as your 1&2C - not something I'm against, but not something I would bank on working or being beneficial to them with no backup plan, as you are advocating - that hardly changes Tierneys role at all. He goes to 15 and a half minutes instead of 17 and a quarter. No big deal. And, if they fail in that role, or get injured (they will), you have someone who can actually play with your wingers and not be a black hole.
It's clear to me that you just dont like Tierney, though - either that, or you play NHL20 franchise mode with injuries off.