You will have some stretches of gravel due to construction. You'll receive mixed answers, I believe. We drove up on new tires to Alaska with no issues and many do, especially those with big motorhomes because they typically don't carry spares - tires are too heavy.
Then there are others that take two of everything... just in case. Do whatever feels comfortable for you. Very few people get flats on the trip and very few get broken windshields.
The best suggestion is to drive slow, especially through the gravel areas. This is one trip you can't rush. Have a good one!