Cambridge South station was always intended primarily for inward travel to the hospital/biomedical campus.
This is correct. Cambridge South was never designed to have any car parking provision. The Biomedical Campus already has more than 20k employees, with more expansion planned. There is also a lot of people going to the hospitals as outpatients or to visit inpatients. The main purpose of the new station is to get those people off Cambridge's congested roads and onto the trains.
Personally I don't see why they didn't put parking there, though. There's room and it might have been useful to those driving in from the south intending to go to London, and reducing congestion around "City" a bit.
There is nowhere to build a station car park, all of the nearby land on the campus side is already allocated for other uses, and there is no road access on the Hobsons Park side.
There are significant access issues too, especially the need to keep the campus roads clear for blue light traffic to the three (soon to be five) hospitals.
It's not relevant for park-and-ride-to Cambridge traffic, though, as Trumpington handles that.
Trumpington is the most convenient Park and Ride for Cambridge South, Stagecoach route A provides a direct link. It has 1600 spaces.
No doubt there would have been some people who previously drove to Cambridge Central, and would’ve driven to Cambridge South, but instead found themselves cycling or taking public transport to get there instead.
Parking at the main Cambridge station (333 spaces) isn't very attractive because of traffic congestion. The main stations with parking for villages in Greater Cambridge are:
Audley End 662 spaces
Royston 517 spaces
Cambridge North 428 spaces
Whittlesford Parkway 348 spaces
Perhaps we can use the space that would have been used for parking next to Cambridge south for housing instead.
It s more important to use campus land for hospitals and laboratories. Any car parking on the biomedical campus needs to be for hospitals and laboratories too, not train passengers.