What is the actual problem with illegal immigration?

That illegal immigration is bad gets a lot of media attention. I understand that when there is illegal immigration, it becomes hard for a society to collect data and administer things like taxes and entitlements. This is the only problem with illegal immigration I can think of. People can critique immigration generally--for example, claiming that immigration is associated with crime or hinders the preservation of culture--but these criticisms are of immigration generally and not illegal immigration specifically.

Are there problems with illegal immigration other than that it makes it difficult for the government to do things like collect taxes?