That's not a hypothesis. Modern psychological care has tested, verifiable positive effects on mental and physical health.
To say a person living in the past would not also benefit from mental health care simply due to the date range of their existence is absurd.
You may as well say Tommy John surgery wouldn't help a 1930's baseball player.
Benefit from mental health and improve their play isn't the same thing.
Are you guaranteeing that a sports psychologist traveling back in time would've helped players in the 60s/70s play better sports? Feel free to present studies/data to support your view (especially those that have been replicated), I can be won over. I think it's very hard to say how a new psychological modality would've affected players (people in general) in the past.
If the whole group of sports players had access to a sports psychologist and it returned positive gains, wouldn't the whole filed be elevating their play, so we'd see the same approximate deltas between average, good and great players?