This will just lead to more part-time work and fewer people getting benefits. Maybe more off-the-books work, too.
Not really, in fact this may improve hiring. This affects people who are asked to work over 40 hours a week, but receive no additional compensation. This has long been a dodge of businesses and nonprofits who push for ridiculous hours, but don't compensate accordingly. Under the old rules, workers over the threshold can be worked as many hours as needed, but will only get paid for the 40 hours their salary is based on. This allows companies to avoid hiring additional staff since all those hours you work after 40 are basically free (at least to them, you end up exhausted, stressed and miserable).
When workers actually receive pay commensurate with the time they put in, companies will have to take a look at their staffing and work structures and make sure that they have enough people to do the job rather than wringing hours out of underpaid and overworked staff. If a company realizes it has staff that should actually get paid for the work they do they will have three solid options: 1) hire more staff to get the work done without overtime 2) pay those salaried people enough to put them above threshold or 3) improve efficiency so enough gets done in 40 hours that you don't need to do a big hire or raise wages.
In all three workers win either more jobs, more time, or more money.
Threats that companies will have to put everyone at 39 hours just to make sure are mostly bullshit scaremongering. Those that would choose to be dicks about this are already being dicks about hours to avoid providing health insurance.