Why should states with significant immigrant populations designate particular seats in their legislatures (i.e. Parliament, Congress, etc.) to...

(In this answer, I assume that you are using the term "state" the way that political scientists use it.  In this case, "state" means the same thing as "country.")

Of course, not all people will agree that states with significant immigrant populations should designate seats in the legislature to represent that particular group.  However, if we have to argue that states should do so, we can say that designating seats will ensure that immigrants’ concerns are heard and will make immigrants more likely to feel connected to their new country.

In democratic countries, people want to have their voices heard.  They want to feel as if they have a say in how they are governed.  For this reason, it is good if people feel that they are represented in the legislature.  It is also good from the country’s point of view if all voices are heard.  If there is a large group of people in a country with a particular grievance or need, the country is better-off if it knows that that grievance or need is.  If the government knows this, it can do something about the problem before it gets worse.  Thus, it is better for both the immigrant group and the country as a whole if the group is represented in the legislature.

If a country has a large immigrant population, it will want that population to feel connected to the country and it will want them to assimilate.  If you have a large group of people in your country who do not feel that the country is really theirs, your country will be weaker and less cohesive.  The same is true if you have a large group of people in your country who have not assimilated and do not share common beliefs and values with the rest of the country.  Giving immigrants seats in the legislature can help prevent this problem.  If immigrants have their own seats in the legislature they will feel they have a stake in the country.  They will feel that the country cares enough about them to give them representation.  Because of this, they will feel more connected to the country and they will want to assimilate.

While not everyone will agree that immigrants should have reserved seats in the legislature, there are certainly good reasons to think that they should have those seats.