You’re saying that you just dump trash straight into the inside bin and then empty that straight into the outside bin without ever using a bag at any point? You do whatever ever you want inside, but for the outside bin, it depends on your jurisdiction and who holds the contract to collect refuse. In my county, and per rules of the refuse company that hauls the trash, all trash must be placed in bags inside the bin. Unbagged trash is not collected, as in, they literally will not empty the bin until you bag it.
Also, unbagged trash has a higher chance of spilling when it’s dumped into the truck. Our trash always makes it into the truck, but a lot of recycling ends up in the gutters or blowing down the street because it’s unbagged.
I also limit what goes in our trash and only put out a bag or two a week. And our city is in charge of refuse and recycling but they contract out with a waste management company - the city doesn’t have its own dump or recycling facilities (and this has been my experience in cities big and small across the country.
I watch the trash and pickup process a lot (because of a toddler) and what I’ve noticed is that bagged trash gets picked up out of bins and thrown into the truck while the recycling gets picked up by the “arm” and dumped; that’s where the spillage comes from.