That isn't what's causing the problem. It's that demand is greater than supply. Rent is lower in rural areas becuase nobody wwnts to live there. Even if rent was free you would have the same problem that there simply isn't enough housing. Immigrants almost invariably live in cities, and they do drive up prices.
I used to work for a government employment centre. It was depressing how many highly educated people emigrated to Canada for promises of a better life and ended up driving Ubers because they were mislead about earning potential or education equivalency.
and thats why allowing immigration to give them a chance of "a better life" is IMO unethical.
I've met a lot of smart immigrants who left their country because there was no opportunity for them to contribute or improve. Often there's so much corruption or racial/religious discrimination that it's a choice to sink or swim.
Of course, the prospect of "a better life" even in the most dire circumstances is becoming less attainable when the local population are already struggling. I've seen several articles similar to this one, where the reception from people is "I'm struggling to pay my rent too, why doesn't anyone do a story on that?"
https://ottawa.citynews.ca/local-news/ukrainian-newcomers-st...
And lower demand by restricting immigration.