I can understand why the OP may NOT want to "T" into his camper propane line. With an external propane tank, you can take the tank and grill anywhere, and are not limited to just the length of hose between grill and trailer. If you want to have a cook-out at someone else's campsite, it's very easy to set up the stove elsewhere.
We have on occasions (in the past), used our Coleman stoves and propane tank on family get together's to serve as extra cooking surfaces. It worked out great! We also had a Coleman propane tree with the gas Coleman light that affixed to the top....great for fishing on the bank of the lake at night. So the extra, "transient" propane tank DOES come in very handy for those who use them this way.