This is more in relation to flights which have a single class of passengers with a short haul flight duration. Why don't airlines adopt random seating arrangement i.e. first come first serve basis. We already see business class passengers of having the flexibility of boarding at their own convenience.
This might solve the problem of boarding, and might also encourage people to board quickly.
To solve the issue of cabin baggage, we could have dedicated space for each passenger, by dividing the existing baggage space by the number of seats below. This would take care of 'greedy' passengers. Also, passengers can check beforehand if they are carrying excess luggage.