It only makes sense to use an antique fixed-segment LCD if you know you will not face any market competition. It's a hobby project in that case, not a commercial one.
..or you care about power consumption.
Or long-term security of supply
Or cost.
Or sunlight readability.
I'm skeptical about the middle two, certainly. When you design something with a weird part -- and a custom LCD is certainly a "weird part" -- you are at the mercy of your supplier, specifically future changes to their minimums and lead times. Cost-wise, the best way to attack that problem is just to assume that you'll have to hit alibaba.com every so often to find the next big load of surplus panels that someone's dumping on the market.
Power consumption... well, it's a power supply, isn't it?
Sunlight readability was one of the many Achilles' heels that was going to sink the iPhone, as I recall.
(Edit: yes, I know, the decision's made and no longer open to debate, which is fine. But I couldn't resist posting the link to the Kenny interview, since Dave seemed so receptive to his point at the time.)