Would Libra have gotten the same regulatory pushback if they focused on just building a chain (with USDC issued on it) and not a stablecoin?

probably not.

launching it as "the new global reserve currency" is probably what did it more than anything else

IMO the timing of expansion into crypto on the heels of 2016/Cambridge Analytica hurt them far more than any product specifics (they were right in the depths of the villain arc)

Given the timing I think it might have, only because it would have lent credibility and distribution to too many people and the last thing they wanted was to provide those kinds of rails to billions of users across borders and without their oversight and control. Libra's mistake was they just gave them too large of a target to snipe them right out of the gate.

libra might’ve dodged some heat if it stuck to chains, not coins!

Probably not, focusing on building a blockchain without a stablecoin would likely have faced less regulatory pushback.