We went to Alaska with only 5,000 miles on our OEM tires and the factory spare on our travel trailer. We had one trailer flat on our 10,000-mile trip and that was due to a screw through the sidewall just above the tread. Therefore, it couldn't be repaired and I had to buy one new tire in Wasilla.
We came back via the Top of the World Highway and had no problems with those OEM tires despite traveling over a section under construction that was covered with 6" chunks of broken rock. However, about 5 miles after crossing the border into Canada, we had two flats on the rear axle of the truck. I replaced one with the spare and the other was plugged and filled by a wonderful lowboy driver who stopped to offer his assistance. We drove all the way to Whitehorse on that plugged tire before getting two new Goodyears at Walmart.
I wasn't quite as helpless as this makes me sound because I had a full set of tools, a 12v compressor, a partial set of tire plugs (I had unsuccessfully tried to use some of them on the trailer flat), and a can of Fix-a-Flat. But the time it would have taken me to plug and fill the tires with my equipment was shortened considerably by that truck driver.
However, I highly recommend that everyone going to Alaska take a compressor, Fix-a-Flat, and a plug kit whether you have new tires or not. In fact, I still carry that equipment with me on every RV trip in the Lower 48 in our new 5th wheel.
