I don't know if it's the same in the US, but every job in Australia generally comes with a 3-6 month probationary period where employment can be terminated for basically any (non-protected) reason with little notice. I've observed that the option to do so is seldom used - probably because there is not usually much incentives for managers to decrease their number of reports unless there's serious problems.
Most places still interview. Because hiring someone for 3-6 months is still an expense. For large companies, onboarding can take many weeks before you're even thinking about being productive. Interviews don't need to be 100% accurate. They need to be time-efficient and an ok filter to prevent hiring the worst people.
I don't see how a bad job market is going to make skilled people be willing to intern in order to get employment. Employment is a market, if demand goes down, then the reaction will be that price goes down.
The reason students are willing to intern is because the supply is so high and demand so low that you can effectively hire them for nothing (or next to nothing). The interns know that on completion the internship will upgrade them to a new category with new supply/demand. It's the same reason they are willing to pay large amounts for a university degree.
So interviewing will stay the same. If demand collapses, we will see wages drop, and I imagine the supply of software people will react through early retirement, career switching and reduction of people choosing it as a career before we see an upheaval of hiring methods.
That probation period never ends in the us. You can be fired at any time for nearly any reason.