It costs companies a lot both monetarily and in time/effort to advertise job postings, get applications, schedule interviews ,hire someone new to do the same job, train them and get them set up and acclimatized until they become productive. If they can still have them working that'd be a big boon for them. Of course this won't happen for all jobs, but is likely to apply to a large fraction.
Someone making a conscious decision to hire in another country takes a lot of effort, but an existing productive employee who is already working 100% remotely for the past 6+ months asking if they could work in Canada or India till the uncertainty around the election is resolved will definitely have a good chance.
You're going to get people who are already productive for the company moving willingly to lower expense parts of the world, while continuing to be identical in disruption to someone moving to Wisconsin.
Companies (more importantly managers) do care about hiring locally, since they have a lot of opportunities to on-board, evaluate and guide - however, once they're all baked in, the shift is less of a concern for the companies.
"Hiring in a foreign country" is different from "We save 18k/employee if they move to Canada and they want to!".
There's a big assumption in "Since remote work has become acceptable". Some companies are talking about making things permanent, others are already trying to get people back in the office.
And if the remote work swing is both big and permanent, then I think this is less likely a "backfire" situation and more of an "irrelevant" one. Companies looking to save money would hire in the foreign country regardless of the new rules.