Because they live in the US, and therefore by law should have representation. (Note that they still can't vote, so the influence is limited.)
Permanent residency is very much a thing allowed by law. Dismissing them as foreigners is a bit harsh, when some of them have been in the US longer (and legally) than anywhere else in their lives.
Sometimes it's not possible. For example an India does not allow dual citizenship, to become US citizen they would have to give up their citizenship.
If your extended family and friend live in India, that might not be an option.
Furthermore, for Greek citizens it is absolutely impossible to get rid of their citizenship. They can burn their passports, commit crime, but they will forever stay a Greek citizen.
As if most Indian citizens living in the US even have an option of getting US citizenship.
There is a 150 year waiting list for someone from India who is here on a work visa to even get a green card much less citizenship.
The fastest route to citizenship for someone from India working here is:
1. Get pregnant
2. Wait nine months for your child to be born in the US
3. Wait 21 more years until they are old enough to sponsor someone for a green card (and don't forget to make sure that their income is high enough to support both themselves and you single-handedly)
4. Wait another year to actually get the green card
5. Wait five more years to qualify for citizenship
Many would happily become citizens but can't because they're not here legally. That's the WHOLE thing the Dreamers group is, they've been here living for most of their lives but were brought here as children but they they can't become a citizen without leaving and waiting 10 or so years to start over from square one.
Permanent residency is very much a thing allowed by law. Dismissing them as foreigners is a bit harsh, when some of them have been in the US longer (and legally) than anywhere else in their lives.