Because in many cases this is not possible. For example when Twitter added polls no other client than the default one was able to display them. If they kept some older version around they would not have feature parity. Then they introduced threads, these would look weird. Now imagine if they introduced nesting, the database model could change in a way that all older versions would require a substantial update. Maintaining an older version may very well mean maintaining two products and two synced versions of the database. Now you have doubled your engineering cost.
It would probably be only marginally more expensive (for Twitter specifically) for them to add changes in a way that's backwards compatible with older clients, so I don't think this argument is particularly convincing. I think, because it's somewhat plausible, they pushed it, but because they really wanted to control all of the clients, to increase their advertising revenue.