The Toyota museum description:
Toyota based its Toyota Publica model on the concept of a domestically produced family car. This car was aimed at the general public with its sensible design and practical styling. However, its simplicity and economical design strayed from the market trends of upgrading to the luxury car. Consumers chose the name Publica as a combination of public and car.
They show a hard top with the roof extending farther back over a second row of seats. The convertible looks like a two seater.
It doesn't look practical, unless practical would be defined as Miata like. But it does look a lot more appealing than the current offerings of tall, five door, not so small, heavier and underpowered for what they should be, cars in the practical classification.