It's not exactly the same as buying a lawn mower from a neighbor. Even states that don't perform a background check still require the sale to be made through a licensed dealer, with a transfer of ownership recorded. Given you can't know what the person will do with the gun (or who they might transfer it to, or get it stolen by), you'd be stupid to not perform an official transfer of ownership on a personal sale.

Will requiring background checks on all gun sales actually reduce the number of guns sold to bad people? Most of these states that don't have background-check requirements for private sales do have laws that make it illegal to sell a gun to anyone who is not legally able to possess one. So these sales are already illegal. Is making them "extra special illegal" going to make a difference?

I'm not actually opposed to universal background checks. I'm just not sure it will have a big impact on overall violent crime. I'm definitely not convinced it will have any impact on mass shootings. Mass shootings are just an incredibly different beast than most other violent crime. I'd say it has more in common with rape than with murder or assault, because they both come from deeply narcissistic world-views. What are we doing about the growing narcissism problem in the world?