In the Cooks Illustrated BBQ brisket recipe and many others I've seen, they call for moving the brisket from the grill where they are being smoked to the oven to finish. I'm wondering why the recipes call for this step rather than finishing in the grill.
Convenience: It's more convenient and easier to monitor the temperature inside the home. The oven has a thermostat, where the grill temperature needs to be monitored and adjusted manually.
No smoke left: Is could be assumed that the smoke has been exhausted.
Too much smoke: The smoke flavor could become too strong if finished on the grill.
There's really no reason to move the brisket into the oven aside from convenience and ease of temperature control, with the contrasting point also being true that there's no rule that says you have to leave your meat on the grill for the entire cook. After a few hours, the brisket will have taken on about as much smoke as it can/should. So if it makes sense to finish cooking it in the oven, there is nothing keeping you from doing so. Also bear in mind that a gas grill is not the most efficient means of cooking with indirect heat. You will use a lot of propane to maintain even relatively low roasting temperatures, while an oven requires far less energy to achieve the same effect.
If it were me, I would be inclined to keep the brisket in the cooker if I were using a charcoal grill, or a smoker, where the cooking chamber is more suitable for retaining ambient heat. I would be less inclined to keep it on a gas grill the entire time, as it's not worth blowing through the bulk of a propane tank for no discernible benefit.
All of your postulations are valid. A couple more below. These would my main concerns:
A normal grill has a tendency to be wilder in control and cooking to the centre properly might become unpredictable. Though I have seen full grill recipes with the Big Green Egg. This you can mitigate using an insertion probe thermometer.
Purpose of the grill is deliver flavor to the outer layer of the meat. It doesn't do much for the center and it tends to dry out the meat in long term since the humidity escapes. In the oven it reaches a saturation point and prevents turning the outside into leather as the center is being cooked. This you can't easily mitigate on the grill. If you look carefully at their picture, you can see a break in color and texture at about 1/2" depth where it goes from gray-ish brown to moist pinkish color. They are trying to prevent that break line to get too deep in the meat.