I don't think it is a fair comparison to say breaking into someone's house is equivalent to claiming asylum.
I also personally just don't understand the issue with increased immigration - it gives us a larger labor pool, and counteracts our declining population.
Given the current policies of the Biden administration, my understanding is that most immigrants are actually going through the legal process of claiming asylum.
Channel 5 did a little mini documentary about it that I personally enjoyed: https://youtu.be/2dQ4-VNaG3s