That seems like an easily solved problem. Perhaps I should have emphasized illegal immigrants. Legal immigrants (i.e. those who apply and receive work visas or the like while still in their country of residence) I don't think most people have a problem with. It's the masses of wanderers who just show up at the border with a bogus asylum claim that drives people bonkers.
So I would argue you are incorrect in your assessment. The centrist parties have just been cowed by wokism/political correctness. IMO that is the main reason they won't move away from lax immigration policies. If you need approved numbers of immigrants to provide labor for certain industries, they are easily obtained and most citizens aren't concerned with that because they feel the government is still in control (and they would be if they are prepared to deny entry to immigrants who just show up).
Finally, centrist parties are starting to wake up to their own stupidity (caving to the small but very vocal woke minority) but much chaos has occurred in the meantime.
Here I would dare to say that your Canadian citizenship blinds you to certain realities of Europe. In other words you are form environment that is cultural mixing pot by default and fairly financially unregulated. In other words when people of color come to Europe legally that is still consider to be a huge problem by many. Since that still "undermines" centuries of history and changes the culture. The fact that it is legal makes little difference to most people. In a sense that is even worse since that seems as deliberate sabotage of nation state, while illegal immigration is simply the problem that has to be solved. All of this is exactly why the strongest of my local centrist parties is at 2%, since to most people legal or illegal immigration doesn't make that much of a difference. Especially since legal immigration tilts labor market and price of labor towards employers. What means that many will not be able to cover their expenses and therefore they will have to move to richer EU member state to cover that. However that only opens even wider need for legal immigration. In other words this is why landscape in Europe looks as it looks. Since in the end this is the game that average Joe can't really win. However typical centrist politician can't understand this since that would crash their whole free market worldview. Therefore since they don't want to change people increasingly say "OK, the far right and nationalists it is".
This is exactly why my nationalists are hoping to expand welfare state and expand domestic production of goods (what demands reductions in free trade). In other words as the most developed western countries are cracking under debt, woke stuff and weaker and weaker public services the idea is to use welfare state to bring back our large diaspora back into Eastern Europe. So that we don't have to import various people from the global South. The process has already started and is indeed showing certain results (Canada will be one if the targeted countries).
However if you want welfare state then again the centrists are a problem and you have to keep them away from power. As I said the fact that they have 2% here isn't a pure coincidence (they are expected to win 0 seats in EU elections). What is especially since here in Slavic world unregulated market of the English speaking world isn't default position. Therefore that is also often considered to be foreign element that has to be controlled. As a matter of fact for older and middle aged people that were born in Communism it is often hard to tell the difference between market and woke (since they grew up without both). As a matter of fact on my left there are voices that want to cut out all immigration as a way to crash globalism and the market. Therefore the odds are that centrists will continue to lose ground, since they have various positions that are interesting to decreasing amount of people. Since the increasing amount of people in Europe doesn't wants globalization on individualistic principles and multi-culturalism of US type (and those two are what Europen centrism is all about in the end). In other words many want supply chains that is more local or regional and made by locals (right), or they they want less market altogather (left). In other words both want to slow things down and centrism wants just the opposite.
This is exactly why for years there is open risk that EU will crack into 2 parts like Roman empire. Since ex colonial powers in western Europe that are increasingly multicultural aren't that compatible with what is today called Central Europe (what is basically ex Warsaw pact). Which is considerably more socially conservative, but often to the left of western Europe in the economics. Therefore if Western Europe is moving away from globalistic centrism that kinda significantly rises the chances that EU will stay together. So all of this is very multi-dimansional in ways that evidently didn't occure to you.
As I said before: I and North American's of this forum live in two different realities.