>>23530431"Gotta catch 'em all" was a tagline that was only used in the west. In Japan, the tagline is "Everyone, get Pokemon!"
Catching them all was never really encouraged. Even in Gen 1, there was no real reward for doing so. Just a still image congratulating you. Now that there's 700+ Pokemon, not being properly rewarded for your efforts is inexcusable.
To answer OP's question, I think the series won't have a definite end. Nintendo/GameFreak will one day decide that physical games are "too expensive" and go full digital. Then they'll make more and more free2play games, eventually overshadowing the main series until they stop making them completely.