I generally have a lot of respect for Eugene Volokh, but he's fighting a straw man in his post on regulating guns like cars. The people who argue for this have in mind especially two ordinary car regulations they would like to see applied to guns, neither of which he mentions.
1) Registration of all cars with the government at time of sale or transfer,
2) Mandatory insurance to cover likely potential costs should you operate it in a way that causes harm.
So that would mean universal registration of firearms, as well as mandatory (and rather expensive) insurance for each and every firearm you intend to operate.
In other words, the proposal is for a much stricter regime of firearm regulation than currently common across the country -- not a lesser regime.