Given that an extended human life (beyond merely being incarnated then dying - which is the minimum and vital requirement for eternal resurrected life) is about theosis - which is becoming more god-like, more divine... then the core argument in favour of the value of reincarnation is probably that it enables more life experience and learning to be accumulated; on the basis that it is hard to suppose that everybody would get enough valuable experience in a single lifespan to enable them to become a god.
Against this, I feel that the following are significant:
1. We existed pre-mortally as spirits, and came to incarnation on earth voluntarily; God placed us each, individually, in a situation which provided what we personally most need for our spiritual benefits. Some people need very little - those who live long lives need a lot.
2. Further spiritual progression is possible after death - so life is not the only experience we get.
3. The nature of the most essential experience we get during mortal earthly life is mostly negative.
What I mean is that, to become grown-up children of God; what we most need is what Heaven cannot well provide - that is experience of sins, vices and suffering; of ugliness and lies; of meaninglessness, purposelessness, and isolation... the many negative aspects of living.
The example of Jesus may be instructive - because his experience in mortal life entailed experiencing a great number of negative aspects.
It seems that negative aspects are necessary for us fully to understand the positive aspects of Good - fully to understand Love, Hope, Faith it is necessary to experience Pride, Fear and Hate; Despair and Nihilism. On earth we experience these primarily as temptations - we do not need to yield to them, but everybody - including Jesus - is tempted by evil; and if, as often happens, we do yield to them, Christ's atonement means that repentance is fully effective at undoing the harm.
So, to return to the idea that reincarnation seems necessary to get the experience needed for spiritual progression; it seems plausible to believe that people get enough suffering during a single mortal life, that not many would need to come back for more.
Note: My belief is that reincarnation is possible, and happens - but it is not usual. Most people have one mortal incarnate life. William Arkle is the main source of the above ideas - however, it should be noted that Arkle himself did belief in reincarnation as the norm.
