You can't say "Well enforcing the rules doesn't impact everyone equally so you can't enforce them!"
If you entered illegally, you need to be sent home. End of logic. Any other variation allows the system to be gamed trivially.
Most of the people who have entered illegally did so because they are prohibited - due to criminal record - for entering legally. They also harm the legal immigrants in their community too.
You can not allow asylum cases and also permit the criminals who created those conditions those legal immigrants fled. You are damning everyone when you do.