Yes, private cars spend 95% of its time idle on parking. One solution is car sharing, which need 4-8 times less parking space: http://svedic.org/philosophy/car-sharing-and-the-death-of-pa...
Public transport is the best answers, but even so rush hours is still hard to manage.
Rush hour is a global issue that could actually be mitigated by more flexible schedules and increase in remote work. So we shouldn't try to solve it by transportation alone.
Interestingly jobs that can't be remote (factories, etc) usually already use alternative schedules that avoid office rush hours.
I have a share in a car sharing cooperative with about a dozen cars, from a smart to a Mercedes transporter within five minute walking distance. Renting a car costs you $3-4 per hour plus 50 cents to 1$ per kilometer (half after 100 kilometers)
The problem with car sharing is that people tend to use their cars all at the same time: morning commute, afternoon commute, evening errands/leisure
Car sharing only makes sense for the occasional use of a car (which happens ca. 5 times a year, when I really need it) and not if you need a car on a regular basis, like getting to work.
But then, it doesn't only make a ton of sense, it also offers very considerable savings at no downside. That, of course, only works when there's good public transport available as an alternative to car ownership.
However it is used effectively in cycle track design. A 4m wide bidirectional cycle track can become effectively omnidirectional at rush hour significantly increasing capacity in one direction.
However, one passenger ride sharing increases total miles driven. So in ultra congested city's it can actually make things worse.
I use bike for small hops, public transport for commuting to work, and occasionally I use car sharing when needed.