Hey @GLePage! Thanks for your post.
From what I understand with Payment Subscriptions, the existing Subscriptionshouldcontinue when the payment method is updated. Do you have any examples of new subscriptions created by just updating a payment method? I’d love to see these for more context.
As for the update payment method link, I agree that sending that manually or through automation would be super convenient. It appears we aren’t the only ones hoping for this either-- check out this existing Idea on our forum. I upvoted it! Be sure to upvote and add your use case to keep the momentum 
Let’s invite some of our experts to confirm that update payment behavior: @danmoyle, @Humashankar, @louischausse can any of you confirm the behavior described here? When a payment method is updated for a Subscription, a net new subscription is created, and the original one is not continued.
Best,
Kennedy