The ability to draw on the ideas of animals is based on physical strength? Regardless, I think this is far too specific a narrative to be pushed on an entire class.
Who said you had to draw on animals? I said "primal" not "animalistic"
The Barbarian of the World Tree draws upon the World Tree. The Zealot pulls upon the Divine. ect. And as for it being strength... why not? Hundreds of cultures around the world gave their strongest warriors mystical powers based on their strength in battle. There is nothing inherently wrong with the concept.
A wizard should be able to apply their intelligence modifier to ability checks that the DM rules are based on intelligence, just as any other character can. They can add proficiency and other bonuses to the specific skills that fit their background and character concept. They don't, and shouldn't, have a class-based bonus to a predetermined set of skills.
And how much of your determination of this is based solely on the fact that there is only a single "magic" skill, and it is based in intelligence?
You are getting hung up on "but strength is only muscles" and not looking at the actual narrative at play here. Which is the barbarian entering a state of heightened focus and physical ability while drawing on the primal source of their rage. Remember, it isn't JUST these skills, but also Athletics, the only strength based skill.
A barbarian who prioritizes DEX or CON over STR is functional but not optimal in combat. There's no reason they should also be worse at skills like perception. (As for WIS as a primary score, I recognize that concept being viable is purely aspirational).
This is really a silly argument. Because let us look at the 2014 Barbarian. Is a Dex-bard worse at perception than a Str-Barb? No. They are just better at dex skills, of which the barbarian really only wants one in general. The entire reason the Dex-barb exists is because people wanted stealthy barbarians.
Now, Dex-Barbs aren't encouraged.... because you can have stealthy barbarians without limiting your combat stats. And Con barbs are still equally viable.
But the crazy thing? Unless you were a Barbarian who was playing 16 Con, 16 Dex, 13 Str and 12 Wisdom.... Every other barbarian EVEN DEX BARBARIANS are likely better at perception than they were before. Because even with that 16 Con, 16 Dex, 13 Str, 12 wis build that forsakes all of their ability to use rage and reckless attack... they will still be able to roll perception with advantage. And any Con Barbarian that went 18 Con, 16 Str... is still doing fine.
No build is actually being made weaker here, it is just that the normal barbarian is getting better in a way that they really desperately needed.