Actually, deep water wells are usually quite easy to shut in by design. They frequently need to be shut in due to hurricanes or infrastructure maintenance. You don't drill a $100 million deepwater well without all the bells and whistles.
Very cheap wells with low production (onshore, say ~10 barrel per day) are the ones that tend to be difficult to shut in, as they're not designed for easy temporary shut-ins.
That having been said, most of the "must produce" issues are contractual. There are plenty of contracts with production quotas/etc. Similarly, pipelines need a minimum volume to keep flowing, and once they're stopped, they can be difficult to start again (inspections/etc, as well as physically starting things flowing).
Very cheap wells with low production (onshore, say ~10 barrel per day) are the ones that tend to be difficult to shut in, as they're not designed for easy temporary shut-ins.
That having been said, most of the "must produce" issues are contractual. There are plenty of contracts with production quotas/etc. Similarly, pipelines need a minimum volume to keep flowing, and once they're stopped, they can be difficult to start again (inspections/etc, as well as physically starting things flowing).