I see at least 1st and 2nd class very often in longer-range public transport, like trains.

That said, I don't think the lack of higher class options is the reason why people don't use public transport. Some other reasons I could think of:

- People (especially once they get used to it), might prefer to travel alone or with people they know (compared to strangers);

- For some, public transport can feel limiting, as you're bound to a limited schedule and predestined routes;

- Public transport can't and won't satisfy all the needs all travellers have, due to reasons above and others;