Sounds like a stereotypical startup opportunity, a problem exists, hard to solve, outsource the minefield to a TaaS (therapy as a service) provider to rake in some corporate contract money.
I don't think its totally out of class as a startup idea, fundamentally you've got a matchmaking service (more or less) and a scheduling system and a billing system and maybe do it online in video conference or something. How to monetize is not entirely clear. I guess you could bill the company one full "screening" therapy hour per year living off the skim of not every employee using the entire hour and most people having a mandatory ten minute talk along the lines of "all is well" annually or whatever while some people end up taking the whole hour (or more?). This is probably not the only possible business model and probably not the only monetization model but it is the first one I thought of. I used dental services as a model for my theoretical therapy model, hang out on a regular basis with the dentist for a short appointment and most of the time he has very little to do for most of the people, but he can schedule a follow up for real work or a referral if the checkup finds a problem.
I suppose there would be interesting conflict of interest issues where the insurance company paying the therapy bills would probably prefer more unhealthy untreated people for financial reasons so they'd actively discourage hiring a company-wide screening service like this. Or, if it can be proven numerically that early diagnosis saves treatment dollars, I think we have an obvious endgame strategy of being bought out by a (mental) health insurance company.
Like most startups the idea is free and not worth much, it'll all be in the execution. It would be interesting to research the competition, the successes, and the failures. It seems like an obvious idea, the past must be full of failures in this field?