I did have a concept for a game that companion locking would work on, but it's a very different structure basically:
Act 1 - there's a collection of quests and side-quests available which leads toward building your party... but quests don't really hang around and just wait for you to take them...
So, off quest A, B, C, and D take quest A and leave area to head to do that quest do it then return to hub and now there's quests C-2, E, F, and G to take. By end of Act 1 you're pulled into a longer-scale quest that's basically you and the companions you already recruited (maybe enough to cycle some out for different side-quests) that goes to Act 2 which leads to Act 3.
Then on replay you can choose an option to set it in same time-line as prior games and run a different set of quests dealing with other problems and maybe encountering tale of your older party now and again.