Sure, but on the other side, the pay for those jobs would also have a bigger pressure on them to increase.

Someone will always have to do those jobs (at least for a long time until when/if machines do them), we shouldn't expect them to be fulfilled only by immigrants willing to take jobs that nobody else wants.

In Scandinavia - up to a degree - those kind of jobs carry a big pay and a set of perks that makes people actually wanting to take them, instead of being a last resort activity. It also helps create a positive view in society about those jobs instead of being a motive for social discrimination.