When you compare Canada, the US or some of the higher immigration countries in Europe to developed countries without immigration you'd wish you'd have price increase problems.
Japan, sometimes hailed as an alternative to immigration is now so poor and old that middle class Westerners travel there like they traveled to a middle income country twenty years ago. If you think Canada is stagnant you haven't been to places where a quarter of the population is aged over 60.
Immigration problems and friction are real but they absolutely pale to the economic disaster that low birth rate aging economies experience. Without significant migration you're looking forward to decades of deflation, politics dominated by people who raise pensions and basically no entrepreneurship. Cultural and housing problems are fixable (just build more housing), dying out is not.