I don’t buy that for a second. Governments always want more control, and this is just another way for them to get it.
If I supported mass deportations, I would simply vote for it and never tell anyone so that I could get what I want without getting any of the flack from the associates of the people who are deported. There's not a lot to gain from telling others you want to harm a bunch of your neighbors, but there is a lot to gain if you can give them the boot and not being perceived as having anything to do with their misfortune.
This obviously doesn’t imply that those who voted for Trump on this basis want to go back to the open border Biden days.
Hence the importance of controlling the narrative by spinning unchecked stories about immigrants eating cats, disproportionate rates of murder and crime, ignoring revenue from immigrants paying taxes, etc.
The fact that sufficient people will vote on immigration as an issue is orthogonal to the realities of laws and enforcement rates and entirely predicated upon perception of such issues.