Rental cars carry costs that I don't have with my own vehicle: frequent transactions, additional liability issues, wasted mileage driven between fares, uncertain transit times, daily cleaning and inspection for damage, commercial licensing and insurance, middle men, management, marketing, accounting, additional taxes, regulations, and covenants. If I leave something important in my car, it's still there the next day. I don't have to worry about vomit in the backseat. I don't face a transaction cost and a delay (or the uncertainty of a no show) to go to work, to drive home, to hop in the car and go to the mall, or grab a bite. I can leave things in my car. I have less exposure to pathogens and pests from surfaces in revolving contact with thousands of strangers from all over the world, lower probability of exposure to cold and flu viruses, fewer vectors for bedbugs to travel into my home.
I can't see rent seekers (esp short term ones) being so far under my costs that after adding their markup, it will be particularly cheaper for me. The 5 year TCO for a Prius (staple of the ridesharing industry) according to Edmunds is a little over $18 a day at 41 miles per day, 44 cents/mile inclusive of insurance, gas, maintenance, etc. The average fare mile on the Peninsula for a cab is $3. I don't see ridesharing companies finding an order of magnitude in efficiencies and still delivering any kind meaningful profit.
Maybe private toilets will seem quaint and ostentatious, and we'll be soon freed from the tyranny of private bathrooms by happier times of public lavatories.