I'm not claiming that Mexico is a middle income country solely because of US immigration restrictions - far from it. Pointing out their trade opportunities would be a valid counterpoint to that claim. I think most of Mexico's economic problems are entirely self inflicted (same as for the US, Venezuela, or most other countries).
And if Mexico's economic problems are self-inflicted then it makes perfect sense not to invite people who inflict such problems.
Note that I never advocated allowing Mexicans to vote; on the contrary, I'd like to disenfranchise bad American voters rather than enfranchising bad Mexican ones.
There's simply no realistic path where people move into a large, modern European* country and remain second class residents with limited influence over the government. This state won't last a single generation.
* USA included by heritage if not by geography
Well yeah, of course their kids would get to vote.
How would an American wall keep Mexicans in poverty?
Mexicans are free to create wealth themselves or by trading with the entire remaining world. They could even still sell to the US or work for US companies, just without moving there.
If Trump was going to cordon Mexico off, there would be something to that argument. But they have access to two oceans.