The defining feature of the BFT is that they can use polymorph spells on their allies, allowing the beefy barbarian man with high BAB and strength to become a super beefy earth elemental and wreck a monster in a single round, as opposed to doing turning the puny caster with low strength a kinda beefy earth elemental.

If you want to be a polymorph/shifter focused combatant, you'll want your base strength to be really high, which isn't easy to do if you also want high INT and high CHA. Consider that one of the strongest polymorph spells there is is Form of the Dragon III, which with Powerful Change will give you a +12 to strength bringing you to a whopping 20...which most Barbarians already reach at level 1.

And keep in mind that even if you did get your strength to 14, if you're just planning on using Powerful Change Bull's Strength, that means you're spending a turn buffing up and then running with your low BAB and hitting a monster; you're hit chances aren't great, and you might not kill it fast enough before the Magus finishes his opponent and then finishes off yours. I know you say you don't care for number crunching and just want to play a character that feels right, but would the situation of "I turned into a Trex and clawed at my foe for a bit before my teammates killed it" feel any more like what you want? Not saying that it shouldn't, just IMO it's hard to feel like a beast when you don't have the stats of one, but maybe that does work for you.

You're correct in that you don't want to play an Arcanist; a Druid will be much more effective at being a shapeshifting beast fighter, and since they aren't as known for buffing you can probably avoid being pigeonholed into that.