The desire for material and immaterial rebirths are not two of the ten fetters. These two fetters are lust for material jhana & lust for immaterial spheres (jhana).
In MN 144, Channa, who took the knife blamelessly practiced euthanasia rather than suicide. Regardless, MN 144 does not say he did not desire another "rebirth". The Pali here is aññañca kāyaṁ upādiyati"aññañca kāyaṁ upādiyati...natthi", which means to not attach to any new "kaya""did to not attach to any new kaya". The word "kaya" means a "grouping" of five aggregates rather than the "physical body". In summary, Channa abandoned/put aside (nikkhipati) the five aggregates without longing for any other type/grouping of aggregates.
For example, the five aggregates of Channa were generating & experiencing great physical pain. Channa ended his life without wishing to be in any other conditioned state.