Many people hold one or more of the following positions:

1. Illegal immigration is bad, and we should do more to reduce it.

2. Immigration (any kind) is too numerous. Eg someone could say "Nashua, New Hampshire is now 17.2% foreign born and I think that is too high." Within 2. there are multiple separate reasons to have the position. One could think that its bad for assimilation, or one could be upset that the Nashua school system's budget increases are almost completely due to having to hire more ELL staff to accommodate the rapid rise in non-English speakers in a school system that used to be almost entirely English speakers. I'm sure there are more complicated examples but I hope that one is easy to understand.

3. Immigration (any kind) is used to lower wages of the working and middle class via labor and program abuses. At the low end, this used to be a leftist talking point (the kind Bernie Sanders once talked about). At the high end, it is grousing about H1B abuses. Despite many agreeing that th program has large abuses, H1Bs are legal immigrants.

Your idea of an "easy solution" doesn't remotely correspond to a solution for people who think #2 or #3. Even for #1, someone who dislikes illegal immigration does not necessarily want more legal immigration, though that used to be a very common view (eg, Bill Clinton in the 1990s, I think George Bush too). If a person believes #3, increasing the number of legal immigrants may simply increase the corresponding abuses.

n.b. the text above is descriptive, not normative.