Technically you are correct. But practically I'm not sure effect is directly correlated - immigrants typically have nowhere near funds to buy property, so instead rent from rent seekers (which itself is huge problem). Some of them also live in much denser arrangements - think someone sleeping in living room, 4-8 people per bedroom in bunk beds.
As person who migrated couple of times it really hurts to come help local economy, pay significantly more taxes and then get accused. For one - my parents will never be able to lend me $100-300k for a deposit. Tons of migrants also have to support extended families back home.
Right, but those apartments are still off of the market. Demand goes up with supply staying the same.
I will say it's a bit more complicated in the US considering how many immigrants are involved in actually building homes, but I very much doubt it makes up for the literal millions of people coming in every year. Are there any (first world) countries that have housing costs going up at a large rate that doesn't have large population growth from immigration?
It's not hard to see that if we're adding a little more than 1 million housing units a year and our population is going up significantly more than that due to immigrants and their children that we're going to have an issue.
As person who migrated couple of times it really hurts to come help local economy, pay significantly more taxes and then get accused. For one - my parents will never be able to lend me $100-300k for a deposit. Tons of migrants also have to support extended families back home.