Suburbans, Silvarados, Avalances, etc.. seem to burn oil. In my book it's no indication of imminent engine failure, unless you allow it to run too low. Personally, if it were just that issue, I'd keep on driving it. I retired from a metro police agency. My observation was that American made V8's use oil after a while. On the crown vic police cars you better check that oil a lot. They will still run great. I have a 1500 Burb and it seems to use a little oil. It's an issue that I don't even think about other than checking it every now and again, depending on how much it gets driven.
Also, if you want to tow with the burb put a transmission cooler on it, replace the hitch receiver and boost the rear suspension with some Timbrens or Sumo Super Springs. Then, and most importantly, pay attention to the weight of the trailer you buy. Don't go buying an 8000 pound trailer to tow with a 1500 burb. It says it will tow 8200 or 8400 lbs but, just don't. Lots of nice trailers out there at 6000 lbs or less with a slide out, etc..
Come to think of it, every car I own uses oil or otherwise burns it. I just discovered the level at which I don't care.. Wow..