Why do they want to be martyrs?
Why? because that's the Christian tradition - its part and parcel of the Christian story, likely inherited from the Maccabees. Robin lane Fox in his great review of early Christian history (Pagans and Christians in the Mediterranean World) devotes a whole chapter to persecution and martyrdom. The concept, he notes, is informed by Jewish literature glorifying the political revolt of the Maccabeans against the Hellenistic Seluicid Empire that then ruled Syria (including Palestine).
After the Maccabees settled down to political independence they introduced some new concepts to Jewish religious thought, their war heroes were presented as martyrs, rewarded for their sacrifice by a place before the throne of God. Daniel was likely the first product of religious propaganda that the Maccabeans used to encourage a willingness to die in battle, (remember those stories of sacrifice?) but the books of Maccabees continued the process. 4 Maccabees (16:25) encapsulates this 'new hope:' " ... Those who die for God, live unto God." This religious propaganda succeeded in giving the 'spear-fodder' of the Jewish revolt a reason to risk death against the might of the Roman army. Three times in the first and second centuries, ordinary Jewish people were called on to risk their lives against the Romans for political objectives. The number of Jewish 'martyrs,' if that is the right word to use when ordinary people were so cynically manipulated by their rulers for political reasons, far outnumbered the later Christian martyrs, who again were often the poorer uneducated ones of the Christian Church, while the more educated Bishops found reasons in the scriptures to discreetly disappear until it was safe to show their faces again.
That's the background to the Christian concept of martyrdom, which is not a popular concept among today's differing Christianities, except among a few 'crazies' like the JWs.
But it can be expressed another way, that is as part of a life of sacrifice. Of course, some witnesses have faced literal death at the hands of some regimes, and such relatively few deaths have been used to the full within the JW organisation, just as they were in the early Church. The thought also informs the witness willingness to die rather than have a (possibly) life-saving transfusion, but as Hebrews 11:36-38, it as more often expressed through a life of sacrifice, " ... while they were in want ..." as the author of Hebrews words it.
By this sacrifice, they believe that they earn a 'greater place' before the throne of God. If you believe it, that's what you do. But once you start analysing that period of history when Christianity had its start, and the great intellectual, social and religio-political ferment that commenced with Macedonian (under Alexander) conquest of the Iranian Empire, and your eyes are opened, then one really questions WHY? That is, what point (why do it?) is there in going hungry, living in poverty etc?