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Yes, it costs, and yes, to make public transit a valid alternative service needs to be frequent all day.

However, all of the maintenance around allowing private transport is also a cost. That includes all of the private costs for car ownership. If public transport is a valid option, then car ownership becomes a choice.

A tiny city might need 100 busses, but how many cars does that replace? What is the full cost of those cars? If everyone made a monthly "bus payment" instead of a "car payment" (actually payments when you add insurance, maintenance, ...), I think we'd find the bus system much less expensive.