I lost my Queen about a month ago.
If the hive is left queenless this long, there is a good chance you now have a laying worker, and you will soon have a colony of all drones.
As it turns out, the Queen I ordered (via mail), never arrived.
Who did you order it from?
Can I assume this Queen will arrive dead if it arrives at all?
Yes, most don't even make it five days in the mail.
Should I just let nature take it's course and let the replacement Queen continue or should I order another Queen?
Most likely nature has already taken it's course, and it's headed down a dead end road.
Why is the replacement Queen sometimes "inferior"?
I have not seen this to be the case in the middle of summer. The only time I have had any problem with supercedure queens is in early or late winter when there are less drones available or inclement weather.
Don't get too specific of where you live in SE Michigan, we might find you...