I stand to be corrected by someone currently on the frontline but I think your summary nicely sums it up in practical terms. There is an additional consideration that despite the best efforts of all involved in an incident response information can, and frequently does, get miscommunicated, misunderstood or confused. By downgrading the level of a distress or urgency call, if that 10 to the -x were by chance to occur later in the flight, there’s every chance that trying to tell others that it’s a full emergency again would be met with cries of ‘No, it’s been downgraded’! I’ve seen something similar happen on more than one occasion. Although it’s counter-intuitive, for the sake of saving a few minutes of external services time, once a ground response has been triggered it’s usually best to let things run until the aircraft lands. Most responders will usually say that it’s all good practice anyway. The only downside is that while attending the airport, external services are not available to respond to other incidents although emergency plans make provision if necessary to move other resources to ensure a minimum level of cover remains available in the surrounding areas. (Note that this is a UK-orientated answer. Always remember that other States are available.)