We full-timed 8 of our 16 years with a 40' motorhome and 8 years with a 33' 5th wheel. Our #1 choice of camping was always in public parks or boondocking on public lands (not WalMarts). We did this 95% of our stays in 16 years. We made very few reservations even down the Oregon coast staying in the state parks. We only moved on Monday-Wednesday or Thursdays and got to campgrounds in the mornings when folks leave. Some places don't even accept reservations and there are always cancellations to be had.
We had absolutely no problems fitting in and many of the places we used with the 33' & the 40' and stayed in many with both sizes. This includes national parks such as Yellowstone, Grand Teton, Glacier, Grand Canyon, Zion, Bryce and many more. It also includes national forest campgrounds and many, many state parks.
Get what you'll feel most comfortable living in. I see you're from Alaska. We've been there, too - staying on public lands. Plus, the only reservations we made in Alaska for the whole summer were for the July 4 weekend as we found out that Alaskans enjoy camping also, and for 5 nights in Denali's Teklanika campground and for those we just made reservations about 2 weeks prior when we could better judge when we'd be there. It turned out that we were in the Denali area earlier than planned so on a whim we boondocked at a lovely spot closeby and drove into Denali early morning. We easily secured an additional 5 nights at the front campground - Riley Creek.
So yes, it can definitely be done with a 40'! No, you won't fit in all campgrounds but there will be plenty nearby that you can use.
Full-Timed for 16 Years
.... Back in S&B Again
Traveled 8 yr in a 40' 2004 Newmar Dutch Star Motorhome
& 8 yr in a 33' Travel Supreme 5th Wheel