If you dont want to be part of the solution, you are part of the problem.
In which case you've just argued why the right should just give in and do what the left want. Since you've already established that there is no way in hell the left are going to do what the right want, the only solution that stands any chance of ever being implemented is the one the left want. You can argue that the restricting immigration solution is more effective all you like, but if it never happens it isn't effective at all. So given that we have a solution that you admit yourself might work, which might be implemented and a solution you believe would work but will never be implemented there can only ever be one choice.
So throw open your countries borders and start working on integration or you are part of the problem, right?
You are assuming that just because the left opposes the more effective solution means it has no chance of ever being implemented. The right can gain political power at the expense of the left and implement it without their cooperation - the right is already gaining political power all over Europe. I am not 100% sure this is how things would unfold, but I am even less sure of the viability and success of the leftist solution, so working towards the right's goal is still the best course of action.
That does not mean we cannot try the leftist integration solution in the meantime/alongside - the two are pretty much orthogonal, we can do both at the same time.
Even when we were discussing this topic for the first time, I have stated that the ideal solution would be to seal the borders while at the same time to treat immigrants really well. But, we dont live in an ideal world, and if I can choose only one of those options, I choose the more effective one - seal the border.
And one more thing, European right is pretty tame and even if it gets to power and achieves its goals, Europe as a whole will still be among the most inclusive and integrative places on the planet for immigrants. I dont even know what more we could do that we arent already doing...