Why would somebody play an non-caster?

[Psyren]

Yeah, but if you dogmatically follow the tier system

Why would you dogmatically follow anything? When I read that, I see "yeah, but if you turn your brain off..."

The tier system is just a tool to give you a rough idea of what class A will be capable of, and what kind of campaign will fit them best. It's a starting point for the DM to start making adjustments as needed, not an end point to tell the player "and therefore, play X or you are doing it wrong."