Symptoms: all threads in BackgroundScheduledPool busy, lot of tasks in replication queue, none of the tasks is executing. 

![Screenshot from 2021-04-16 16-21-44_](https://user-images.githubusercontent.com/1549571/115193796-e767d600-a0ec-11eb-887c-5c9c2412e50c.png)

Related to #16895

Possible workarounds (poor options): increasing the background_schedule_pool_size to huge values, or restart server every time when that happens etc. - 

String reason;
                if (!canUsePolymorphicParts(copy, &reason) && !reason.empty())
                    throw Exception("Can't change settings. Reason: " + reason, ErrorCodes::NOT_IMPLEMENTED);
            }
            if (setting_name == "storage_policy")
                checkStoragePolicy(getContext()->getStoragePolicy(new_value.safeGet<String>()));
        }
    }
    for (const auto & part : getDataPartsVector())
    {
        bool at_least_one_column_rest = false;
        for (const auto & column : part->getColumns())
        {
            if (!dropped_columns.count(column.name))
            {
                at_least_one_column_rest = true;
                break;
            }
        }
        if (!at_least_one_column_rest)
        {
            std::string postfix;
            if (dropped_columns.size() > 1)
                postfix = "s";
            throw Exception(ErrorCodes::BAD_ARGUMENTS,
                "Cannot drop or clear column{} '{}', because all columns in part '{}' will be removed from disk. Empty parts are not allowed", postfix, boost::algorithm::join(dropped_columns, ", "), part->name);
        }
    }
}
void MergeTreeData::checkMutationIsPossible(const MutationCommands & , const Settings & ) const