Next recurring occurrence starts only after completion

Agreed, wouldn't want to see the current option go away as part of this. I can think of a few different scenarios where I'd prefer to have a fixed recurring date, and some where might opt for the relative date requested here (which I think is what's being asked for, as an add-on versus a change from the current system)

Yes — this should be an optional setting, not a replacement. Fixed-date recurrences work well for routine commitments, but for “start-when-ready” tasks you only begin when you have the time or energy. If youbstart late or if a task takes longer than expected, the interval until the next occurrence shouldn't shrink (e.g. for service intervals). Making the next instance scheduled relative to the completion date (Done date + interval) avoids premature scheduling and keeps future due dates meaningful