Having experience as a front desk agent, I can say that your room rate doesn't influence the type of room you will get. The main thing is the room category you booked into along with the number of rooms of that same category that are available on the day you check-in. Your preferences can play a role as well especially if you request a room away from an elevator, smoking/non-smoking, etc. If you are a frequent guest, most FD staff (including mine) memorize your preferences or look at the notes on your profile which at times has information on your likes/dislikes when assigning a room. There are some guests who request a specific room so we always try to accommodate those requests.
When it comes to upgrades especially suites, we tend to upgrade those who are frequent guests, have a package booking which mentions an upgrade, or randomly choose a guest from the arrivals list.
Also, there are some hotel PMS (Property Management System) that auto-assign rooms based on room categories and preferences...