This is exactly what I did until last year, when the 5s came out. Carried a flip phone with me at all times, and added the iPod touch (which was a hand-me-down from my wife) whenever I thought I might need access to my apps.
The flip phone was a generic AT&T ZTE phone that cost $18 for a refurb unit, and I used the $0.10/minute prepaid GoPhone plan that automatically refilled $25 every three months. I rarely went over on my voice minutes, and actually had to give up about $50 in rollover credits when I bought my iPhone and switched to T-Mobile. Never paid more than $120 in any given year for cell service.
If I needed data for the iPod touch, I would keep a database of wi-fi hotspots loaded up or borrow the shared mi-fi device from my office.
I went with this combo, because I thought smartphone plans were outrageously expensive and loaded up with all kinds of tricks and traps designed to lock in and fleece customers. The added functionality of a smartphone didn't matter to me if I felt the carriers were playing a game to see who could ream their customers more for the privilege of carrying a smartphone.
It wasn't until better prepaid and contract-free plans for the iPhone became available early last year that I considered buying a smartphone. With T-Mobile's $30 100 min/5GB prepaid plan, I pay just over $400 a year for my cell service. Pretty good, even though it's more than triple what I paid before!
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used iPod Touch 5G 16GB: ~$150
dumbphone: ~$50
used iPhone 5/5c 16GB: ~$250
service cost: same
I'll take the iPhone, thanks.
Service cost for feature phones though is not the same, especially if you go the prepaid route. On AT&T, my service charge was $25 for three months of service at $0.10/min. I only went over my minutes when traveling, and still wound up paying no more than $120 in any given year. And both phones I had with AT&T cost $20 or less.
Functionality is one thing, but cost is quite another.