Switzerland mostly does this. I can buy a time-limited ticket from any ticket vending machine which is valid within a certain area, for a certain amount of time, and I can then use that ticket on any bus, train or tram, regardless of company or how many changes I need to make. It's also valid for most cablecars and boats. It's completely changed the way I use public transport.
(You can actually use the ticket vending machine by the bus stop near my house to buy a ticket which can be used to go by bus from my house to Zürich station, then by express train from there to a station in the mountains, and then by bus up to a ski resort car park, and then by cable car from there to the resort proper, and then by chairlift from there to the top of the mountain, and then it's your ski pass for a day's skiing, and then it takes you home again. One ticket.)
(You can actually use the ticket vending machine by the bus stop near my house to buy a ticket which can be used to go by bus from my house to Zürich station, then by express train from there to a station in the mountains, and then by bus up to a ski resort car park, and then by cable car from there to the resort proper, and then by chairlift from there to the top of the mountain, and then it's your ski pass for a day's skiing, and then it takes you home again. One ticket.)