Receiving money for something you wrote 1 week ago doesn't encourage you to write more. It's the knowledge that you will receive money for next thing you wrote that incentivizes you to write more. And a 50 year payout should obviously provide more incentive than a 6 month payout.

There's going to be a point of diminishing return where adding extra years doesn't provide enough extra incentive to justify the cost, but I haven't seen any convincing evidence that 50 years is over that threshold.

The same holds true for copyright extending past the author's lifetime. Especially if an author is older, the knowledge that their children will benefit is certainly an incentive.