I agree it's probably not a right, but we've made it so obtusely difficult to do. Even people doing the process legally have stints where they'll probably quietly overstay visas because the gaps in processing things messes up their status.
Having such a messed up system only leads to more people being undocumented and our society in a worse place. Make it easier to be documented and obvious that not having documentation means you're probably doing something really bad, and we'll be in a far better place. Add in some carrots to encourage cyclical migration while we're at it.
Make it really illegal (read: executives/owners in prison) for hiring undocumented workers. This will do a lot to prevent undocumented workers.