Not sure I follow your math. The cost of an iPhone 6 is (minimally) $699. If you buy under contract, you can't change phones every year. Plus, most plans contract price for service is higher than the cost of the same service plan out of contract. ATT for instance, is $40/mo under contract for service (per line) and $15 not under contract. That's an extra $25/mo for a contract phone. So $200 for a contract phone, plus $300 "premium" for service, your first year you've paid $500 for that phone. Break the phone in the first year, the ETF are more than $200 for most carriers I've seen, so now that phone has cost $700+. At that point you can get a new phone, but $700 isn't $250.
Some of your numbers are off. AT&T charges $25/month for an off-contract line, unless you're one of the few on a 10GB+ share plan. Additionally, an off-contract phone costs $649 at a minimum, not $700. Also, you can upgrade every year with an on-contract phone, you just have to pay the $250 (approximate) service cancellation fee. If your previous model is still working, you will receive around $250-$350 trade-in or resale value for it.
So lets analyze the cost value of the carrier and Applecare+ replacement plans.
Initial cost Applecare+ = $99
Cost per repair = $79
Carrier insurance cost = $10/month
Cost per replacement = $199
Total cost 1 year = $120
Total cost 2 years = $240
Total cost Applecare+ and Carrier insurance, 1 year = $240
Total cost Applecare+ and Carrier insurance, 2 years = $340
Broken Screen:
Cost of broken screen with Applecare+ = $79
Cost of broken screen without Applecare+ = $109 (4.7")
Savings with Applecare+ = $30 per incident (2 incidents max)
Cost of broken screen with carrier insurance = $199
Cost of broken screen without carrier insurance = $109
"Savings" with carrier insurance = -$91
Broken Phone
Cost of broken phone with Applecare+ = $79
Cost of broken phone without Applecare+ = $299 (4.7")
Savings with Applecare+ = $220 per incident (2 incidents max)
Cost of broken phone with carrier insurance = $199
Cost of broken phone without carrier insurance = $299
Savings with carrier insurance = $100 (2 incidents per year max)
Stolen Phone
Applecare+ -> Doesn't cover stolen phones.
Cost of stolen phone with carrier insurance = $199
Cost of stolen phone without carrier insurance = $650+
Savings with carrier insurance = $450+ (2 incidents per year max)
Max Savings
Max Savings with Applecare+ = $440 (2 completely broken phones)
Applecare savings with 2 broken screens = $60
Applecare savings with 1 broken screen incident and 1 broken phone incident = $250
Cost (2 years) = $99
Max Savings with carrier insurance = $900+/year (2 stolen phones)
"Savings" with two broken screens per year = -$182
Savings with two broken phones per year = $200
Cost = $120/year
Conclusion
It all depends on how likely you are to break your phone. If you use a case, a broken screen is almost an impossibility. Your only two risks would be water damage and loss/theft. Those are really easy risks to mitigate. However, if you live some kind of high risk lifestyle, it may still be worth it.
If you use a case and solely buy Applecare+, you're essentially paying $99 for the likelihood that you will get water damage over two years, or have a device malfunction after the 1st year. Theft isn't covered.
If you solely buy carrier insurance, you're basically not covered for a broken screen, since the deductible is higher than the repair cost. Additionally, the savings from a broken or water damaged phone ($100) is less than the annual cost of the insurance ($120). So you're primarily paying for the theft insurance, or for the likelihood that you'll break your phone more than once per year.
If you buy both, you're paying $220 for one year of coverage, and $340 for two years of coverage. That would only make sense if you lose a phone more often than once every four years ($650 savings), break a phone more than once every year and a half ($220 savings), break a screen more than 10 times per two years ($30 savings), or some combination thereof.
NOTE: AT&T's insurance cost appears to be slightly lower at $6.99/month. The device replacement fee is the same. So the cost/value analysis would be slightly more advantageous.