Side question: How many people have had, or heard of, a wizard character reaching tier 4? It just seems that with the wizard's low hp and AC, it would be hard for them to survive that long.
It's true that the bulk of Tier 4 PCs I've seen have been Barbarians, plus a Moon Druid.
My current Runelords game has 4 PCs at Tier 4:
Shieldbiter, Dragonborn Totem Barbarian-20 (from 10th)
Claw, Goliath Totem Barbarian-18 (from I think 8th)
Sandor, Human Totem Barbarian-17 (from 1st, but skipped level 16)
Quillax, Human Moon Druid-18 (from 1st)
The only other PC I've seen reach Tier IV is
Hakeem, Human (Altanian) Berserker Barbarian-20 (from 1st)
Yeah, so bit of a pattern there.

When players play 5e Wizards I ask them to be sure to pay attention to survivability - Mage Armour + Shield are pretty much no-brainers.