Tamils are good and old friends of the US.
Tamils are the ancient people–perhaps the earliest inhabitants–of Sri Lanka and deserve to be allowed to live peacefully and safely in the land they have always occupied.
Since the best natural harbor in Sri Lanka (Trincomalee) is in the Tamil area, the US should consider the strategic value of having friends in this location.
It will help the US to get highly educated and hard-working Tamils as trading partners. Especially, they should consider outsourcing to Tamils.
The Chinese are cultivating a mutually beneficial alliance with the Singhalese majority government in Colombo. As China grows in strength and assertiveness, the US might find it beneficial to have friends in the Tamil portion of the island. That is another reason the US could benefit from a friendly relationship with the Tamils.
If the genocide of the Tamils is allowed to continue, one result will probably be to exacerbate the Tamil refugee problem that already affects India, the UK, Australia, and Canada. The numbers of refugees will go to many millions. It will not be a problem the US can ignore, and it will be much harder to deal with when it is uncontrollable.