Why?
If a person wants to die. Let them. Now if you meant by "tough time justifying" that we humans aren't prepared to allow for this state of affairs, I suppose that that is correct. Nevertheless, let them. Our existential horror is just that: Ours. Their existential horror, apparently, is to continue living.
(I say 'apparently' because it is important to note that while we've walked a long road with our daughter, it would be a mistake to say we 'understand' our daughter. But, I'd venture that we understand these circumstances more than those that think that platitudes are all one needs. "Let go and let God". Bah. Superficial codswallop.)
ETA: I should add that I agree that checks and balances are called for (some doctor input). I'd hate to think that, ala Romeo and Juliet, some hapless person made a stupid decision on fleeting circumstance. Nevertheless, where the state of affairs is chronic ... what's to justify? The fact that is chronic is justification enough (YMMV).
...I do think that mental health conditions and physical health conditions would need to have a different medical approval process.
For instance, if a person has stage-IV metastatic cancer (and are in the late phases with metastasis to brain and respiratory system), if that person would prefer to end it and not suffer for 4 weeks needlessly (only for the same outcome at the end...IE: death), that should be pretty cut and dry and wouldn't be subject to that much review.
Mental health situations need a little more review and TLC I think...
For instance, a person merely coming in and saying they're depressed and don't want to live anymore, I think several aspects would need to be reviewed.
1) are they even being medicated for it?
2) if they are on medication, did they recently abruptly quit taking it instead of tapering down?
3) did they recently change medications and are having adverse effects because of it?
If all proper medicinal interventions are being followed, and they're still just not right and suffering, then sure, it should be an option that's on the table for people.
However, it would be unfortunate if a person (who was fine otherwise and living a reasonably happy normal life while on the right medications) went through with that simply because they either stopped taking their medications and are currently unbalanced, or because a doctor had switched their medications and they were having a bad reaction to it. (which can sometimes take a few weeks during the adjustment period).