Why can't they? I see people on wheelchairs and elderly get on the bus all the time. Yes walking long distances could be an issue but a good public transport system does not require you to walk long distance. Elderly people usually can't afford to get a taxi everywhere.
There some that can, and some that can't. Some that can innrush our, somemthst can't in rush hour.
And about costs: At least here in Germany health insurance for isntance cover some costs for Taxis (when going to a doctor ... while they got stricter) Also in Germany Taxis have regulated prices in order to give some affordability. (Which is one of the critiques on Uber over here, as Uber can pick the routes they like and can raise prices on high demand, while making it cheap innorder to compete with regulated market during other times in hardly predictable ways, which isn't good for people who depend on working transport infrastructure)
