Did they really all feel they had to die in battle? How would this apply to a Poet or Lawspeaker? Was this religious doctrine something that made them condemn anyone who failed to die in battle, or was it perhaps more comparable to certain provisions in the Bible that no-one pays attention to?
We really don't know anything about the actual practice of Old Norse religion (or religions; Terry Gunnel talks about how there's a good chance that the later sources conflate a number of religious groups into one) or about their afterlife.
The Edda is a decidedly Christian document, and Snorri was very much about recreating an heroic past which might not have existed, so his idea of a warrior's heaven and hell would have played in to his constructed cosmology very well.
But to try to give an answer to on attitudes towards death in a pagan society, we can take the poet Sonatorrek as an example. It is written by Egill Skallagrimsson in Iceland around 960 to remember his drowned son. It also mentions the poet Egil frequently, and also one (possible two) previously dead sons, and has plenty of religious ideas and attitudes.
Egill addresses Odin, his primary god, which is normal for a poet in the beginning and the end. Egill is old and is not expecting to go to Valhalla, which probably was rather seen as a special honor, rather than a duty or obligation. He is sad that he will grow old and await Hel without his sons. He also does not believe he will be reunited with his drowned son, who will be dwelling in the halls of the seagoddess Rán, so there is a third place for the dead mentioned. Although unhappy, Egill reconciles with Odin in the end since he has from him the great gift of poecy.
These interpretations mostly come from Jón Hnefill Aðalsteinsson: Trúarhugmyndir í Sonatorreki.
(The poet Sonatorrek is known from Egils saga, but interestingly, the poet itself does in some ways not fit the story told in the book.)