Delete default profiles from new minecraft launcher (2017-)

Latest Snapshot can be turned off in the advanced settings of the launcher. The same way you turn it on.

Latest Release is basically an easy shortcut to play the last given out version of MC, and it's generated by the launcher itself. As far as I'm aware, and I'm pretty certain, that can't be turned off, no

A possibility if you do want it gone, is to download an earlier version of the launcher that doesn't have this feature (if there are any) or download a fully custom launcher. Or, you can make a custom launcher yourself ofcourse ;)

With what I know (and this might not be much compared to you), I can tell you this:

Latest Snapshot can be disabled by turning off snapshots (though you will have to sacrifice using snapshots in other profiles), and Latest Release cannot be disabled. They want you to have quick access to the freshest version of Minecraft.

Hopefully I helped you with the snapshots bit.