I would think the chain and chain tool are overkill for the riding you're talking about.

Have you broken chains in the past? (Touch wood ... I never logged my miles until I got my new road bike, but) I have to have well over 50,000 lifetime miles and I have never broken a chain. Risk factors for breaking a chain would be if you're a heavier rider with very strong legs - climb steep hills standing - do a lot of sprints - and/or poor chain maintenance/failure to replace a worn chain.

By the time you throw in the chain tool, you may as well throw in spare cables (which take so little space and weight that it's hardly worth not carrying them - you can just toss your old cables into your seat pack for emergency spares the next time you replace them), a hand pump, spare spokes, a spoke wrench and a cassette tool ...

There are a lot of things that can theoretically happen that would leave you walking, but you need to balance the likelihood of them happening - and the amount of hassle or danger it would be for you if they did - vs. the weight and bulk of carrying the kitchen sink around on every ride.