For most families big savings come from having only 1 car in a family/household rather than 2. You then eliminate a lot of fixed costs as well as variable costs by bike commuting.
Having a car for weekend trips, shuttling kids or big item purchases etc is nice, but if I wanted to commute by car I'd need a second car which is way more than total of my bike belongings. I commute with wide 42 tires, they last 3-5000miles, other components much longer, marginal costs from each additional bike commute are tiny. My last $700 commute bike lasted 7yrs and is still fine.