My first hand experience/knowledge : There are core and then there are secondary locations. Although all may be referred to as “core” for your team. If the applicant does not live in the 40 mile radius of any of the listed preferred work locations it does not mean and automatic rejection. You can be interviewed and if selected you will be presented the opportunity to accept the position if you relocate on your own.
The longer the position remains open the more location flexibility gets baked in. New locations open up and the ability to take on a “remote” listed employee exists. It does require the manager to make the case for accepting remotes. But obviously if the slot has only been open 2-3 weeks it’s a tougher sell than one that has stagnated for 4+ weeks and with poor applicants to back it up.
I was in your same boat except now I’m assigned to a site. But “Cores” have changed and expanded. I’m states away from the old list of 5-7 cores (I forget them all now) and 6 hours from what would be considered a large site. Even though my City has three large campuses.
You need to ask your leadership for the latest guidance on sites. Which ones are listed as maintain, which are Growth sites and which ones they want to reduce footprint. Comparing that with your personal location will disclose your near future. Long term 99% of “remotes” will cease to exist. Best bet is to get a location assignment and go from there until your position is eliminated or you move on.