Pretty sure you had a defective Touch ID.
I've owned two 5s's in 3 years. Both worked 99% of the time. I actually prefer the old on to the new one.
Also think there is zero chance the iPhone 7 comes in 4 inch form factor. Apple didn't need the se as an interim product to fill 6 month gap. The fact it has top specs means this phone will be the top of the line 4 inch for at least a year. Hope I'm wrong.
Trust me, I exchanged three 5s's. None of them would recognize my fingerprints after a couple days of use. Delete, re-register, another couple days and then nothing. I just seem to have fingerprints that are hard to track. The first-gen Touch ID sensor could not cope. The first-gen Touch ID on my iPad Pro is useless. The second-gen sensor on my 6s, especially since iOS 9.2, has been like night and day. Works almost all the time, even right out of the shower.
I'm not sure if your second comment was directed at me, but I agree. I think Apple plans for the SE to be a year behind. I'd love for us to be wrong because I really want a 4" phone again.