My 15’’ Air is my daily carry to and from work. I definitely do not find it inconvenient to bring with me every day. If you do a lot of work that you need to spread out on your screen, the 15’’ is going to be able to do that for you.
That being said, I used a 13’’ Macbook for years (first a 13’’ Pro and later a 13’’ M1 Air) and got along just fine.
It’s insurance. If you never need it, it’s money wasted. If you do need it, you’ll be happy to have it. Personally I have never needed AppleCare and I have been using Apple computers since the 90s.
Ask yourself what would happen if the computer was lost, broken, etc. If you can easily replace it, you probably don’t need to buy AppleCare. If the loss of your computer would represent a substantial financial hardship, the insurance is probably a good idea.