I have far too many vehicles up here in Los Anchorage. Plow truck, daily pickup, old pickup that I can't sell for enough money, ATV, etc. I have chains for all of them.
Over the past 5 years (as best I recall), I've only used the chains on anything except the plow truck only once to get out of my 120' driveway, on a slope, in March, when it snowed 12" then rained, then dropped to -5. The plow truck wears chains pretty much non-stop December - April.
Chains are worth their weight in gold on a steep icy hill. Nice to have but don't help as much in "just snow".
You won't need them for your trip.
Have made somewhere north of 20 trips up/down the Alcan (quite a few mirroring the OP planned trip) and only needed chains (that I had fortunately) one time back in the dark ages (79 or 80 IIRC) and that was for traction in the mud.