$52500x.07/52=$70 extra bucks added to the eating at home weekly bill plus an additional weekly cost of $13 for energy/maintenance for the kitchen
I will probably never go this route, I love cooking at home but to say its cheaper then eating out at a restaurant is not exactly true.
I understand that this is just a thought exercise, and in that vein, I still think your numbers are so completely off that they cannot substantiate your claim that cooking at home is not cheaper than eating out at a restaurant. Either that or I am completely misunderstanding what you've done.
Looking at your numbers, the $52500 seems to be the cost of a new kitchen ($30,000) plus the cost you'd save per square foot by not having a dining room ($22500 - figuring 150sqft at $150 per square foot.)
You multipled that by 0.07 (why? what is that number? it's driving me crazy!) and divided by 52 (the number of weeks in a year) to arrive at your figure that a kitchen + dining room = $70 extra per week.
So let's start first with your numbers and then see where we end up.
#1) a kitchen renovation does not need to cost $30k. A quick 'googling' shows that the average kitchen renovation is $15k-20k, though it is certainly possible to do it for much, much less. Even with a general contractor doing the work, I'm going to put this at $10k.
#2) you don't have to buy a newly renovated kitchen every year. Kitchen remodels multiple decades, even if they start looking 'dated' after a while (which can be addressed largely by painting and swapping out cabinet faces every couple decades). I'm putting the kitchen renovation good for 20 years. This means the cost of our kitchen remodel costs $500/year or ~$9/week.
#3) the dining room. This one is a giant red herring. A "dinning room" is nothing more than a room in your house that you put a dining table, and few chairs and maybe a china hutch. Don't want a dinning room? Great! Swap the table for a desk and make it an office. Or put doors on and it becomes a bed-room. Or a game room. Sorry, you can't add this space to your total. Don't want the extra space at all? Buy a home with one fewer bedrooms and then convert the existing "dining room" into a bedroom.
So far... if we accept your annual maintenance costs of $500 (which I still believe is too high) and $250 for added electricity, we come out with this:
($10,000 kitchen) / (20 years * 52 weeks/year) = $9.62 per week. Add the above maintenance and electricity costs and we're sitting at $24.04 per week.
Unfortunately, this is where the thought-experiment really breaks down. Others have said "good luck selling a home without a kitchen" and similar statements. The core of those statements is that when you buy a house, even if you don't use a particular room or feature, it still holds value. Your kitchen upgrade of $10k - $30,000 can be recouped when you sell the home. People who care deeply about such things say you can recoup 70-80% of your costs on a kitchen remodel when you sell. Ignoring opportunity costs, that brings your kitchen renovation costs down to under $3/week.
Then there's the assumption that you must remodel the kitchens just to make them functional. Why can't you live with what's there? I've lived in some apartments with horribly dated and cheap kitchens, but they all allowed me to cook amazing food. A stove, a fridge and a sink is all you really need. Since kitchens in some form are included in almost every house I've ever seen for sale the cost is $0. Maybe $500 for appliances off craigslist which will last for years.
What about if you're building from scratch? You suggested you'd include a large 400 sqft outdoor living space and 'enclose it later' if you wanted to sell. When building from the ground up the cost to install a kitchen is far, far less than a remodel. Pipes and wires can be installed when it's done throughout the house - the extra "cost" of the kitchen is the materials, which you'd spend if/when you 'enclosed' your outdoor living space later. I will give you points for reducing your potential taxes with your strategy, but ultimately it will be more expensive to convert an outdoor living space into a kitchen after the fact. You'll need permits, inspections, walls that will need to be torn-down and insulation put up.
Also - while I love cooking 'al-fresco' (during out kitchen reno we cooked every meal on our grill) - I'm curious what you will do in the winter time. Cook outside but eat inside in your non-existent dining room? This might be ok for places like Florida or southern California, ubt it's not exactly warm outside in January in Richmond VA.
All of which brings us to the original question about whether it's cheaper to cook meals at home or eat out all of the time. The one thing we haven't considered is the cost for eating out vs cooking at home. To keep things simple, let's go with my higher estimate of $24/week for the cost of a kitchen (which includes a full kitchen renovation and your maintenance and electricty figures, but ignores any resale value), and consider a family of 4. The per-day cost of a kitchen would be jabout 86¢ per person per day.
We know there are literally hundreds of good meals that can feed a family of 4 for $10 or less (and under $1 for breakfast). Adding on our "kitchen cost" this puts each meal per person under $3.36. Even this is an over-estimation, since the per-day cost would be spread out over the day (e.g. over 3 meals, not just 1). So - can you eat out consistently for less than $3 per person per dinner? That seems impossible ot me - at least in the US.