I think that Whim (or another Whim type service) can work if you consider the the price of the parking space.
Currently Helsinki has zoning regulations for mandatory parking places that is too high (roughly 0.8 per apartment). The cost of parking place is something like 30,000 - 70,000 euros or more. Assuming that return of capital is 8%, the cost of parking space is 100 - 400 euros per month.
If the mandatory zoning requirement is dropped, Whim style services can become profitable even in the long term.
If you build above the ground, the construction cost can be just $20-30k EUR, but after you factor in the cost of the land, the cost is similar.
The 55€/month is only for Helsinki area residents and subsidized from municipal taxes. Without the subsidy it's over 130€/month.
HSL are also working on a monthly API I believe so I suspect the hassle of having to buy a ticket each time through Whim will soon disappear.
The car rental is not particularly cheap. Have you had any experience with that yet?