Why is it stupid not to accept illegal immigration?
If people can immigrate illegally the democratically elected institutions lose control over who can and can not immigrate.
So? That is not something I am concerned about.
Maybe not, but a lot of other people would be. Determining population policy is an important part of a democracy. Size of population effects the environment and infrastructure, size of labour force affects wages, the ethnic/religious balance has social and political consequences etc. Even if you don't care, why shouldn't other citizens be allowed to have a say in this?
The US is a big country and its multiethnic population makes it easier to blend in for illegal immigrants, but the failure to prevent illegal immigration also has a lot to do with two things:
1) Not wanting to get tough with people hiring illegal immigrants. If it costs enough - incl. asset forfeiture and confiscation of profits - few employers would take the risk.
2) Not having a national population register, where all citizens and permanent residents are registered and national ID-cards.
Both things are political decisions, and would be unpopular in a US context, but it is still things you can do and none of them violate human rights. Saying that you can never reduce the problem with illegal immigration to a manageable level is an exaggeration.
Rewarding people for breaking the law risks undermining respect for the law in other areas and is a provocation to people who consider themselves lawabiding. So dropping border security and letting workers flow back and forth over the border (or staying as long they want) is a problematic solution.