12 feet to the washer isn't nearly the hit that 12 feet to the sink would be, since it's used many fewer times in a day.
Depends on how you use it. It is wise to compensate for long runs by changing habits, that does impact convenience though. We don't run the hot water much at the kitchen sink unless we are piggybacking uses--as in running the dishwasher, etc. I don't do short draws of hot water much there unless it is already hot. So quick food rinses are done in cold rather than defaulting to hot, unless it will be needed shortly, in which case the rinse can be done with cold "hot water" until the hot arrives.
Volumes of high-efficiency washer draws are amazingly small these days, as are those for modern dishwashers. With the fast recovery times of mini-tanks it they'd rarely be run dry by simultaneous laundry/dishwasher loads- the time between wash & rinse cycles is usually more than sufficient unless you're using flat-out hot for both.
They are small compared to the old gear, but still more than the mini-tank can provide in any 2 of 3 scenario I mentioned. They do the mix "flat out" from what I've seen in my new appliances. The dishwasher only takes hot and fills quickly. (Complicating things it does some heating of the water if the temp is not sufficient.) The front load washer on warm seems to be about 50/50. The fill takes a few minutes as it has an interesting protocol of adding a little at a time and turning the drum.
140F storage is lossier, but insulation is cheap (cheaper than beefing up the structure to handle the weight an 80 gallon tank.)
I would insulate anyway, so there is no net gain available from that. I don't see why the structure can't support the tank, just that it must be designed with that load in mind, which is why I mentioned designing for the extra ~1,000 pounds.
The difference in tank life from running hotter is miniscule- the elements don't care what the storage temp is, only the number of heating cycles they run through, which is far more a function of the volume of your HW use than the standby loss.
Doubtful, the retrograde solubility of the carbonate minerals suggests the opposite. The elements will have to run longer to do as you suggest (closer temp approach as well as increased external losses = longer runs), and in water that will produce more scaling at the element (and lines) due to the temp being called for. Corrosion of the tank will occur more rapidly at higher temperature, that's something that has been a given in the heat exchange equipment I've worked with. If there is fouling and corrosion related to it or other aspects of water chemistry, temperature almost always works against you in attacking the vessel. The temperature range you are talking about is above what I would normally have targeted in design if I could avoid it--particularly for fouling service. About 50 C (122 F) was a breakpoint at which bad things began to happen at an increasing rate. 20 F delta is typically huge when comparing corrosion rates or solubility.
(If you add an R13 wrap to an R20 tank you'll have mitigated the difference in standby loss anyway- the duty-cycle of the elements will be about the same.) Liming/scaling deposits go up slightly with temp, that's about it.
It's a logical fallacy to suggest doing the wrap on one tank and not the other. As indicated above, the higher temperature has some major holes and not just surface insulation.
I pointed out the mis-statement "Surface area and losses won't scale 1:1" because your explanation for had to do with volume, which is not a standby loss factor. Standby losses are INDEED roughly 1:1 with surface area, quite independently of the fact that losses aren't linear with volume, which is where your explanation seemed to go.
What I said was accurate, not a mis-statement because I qualified it. I intentionally avoided going into a detailed dissertation and explained why in the 2nd sentence. Cherry picking it as you did is BS. As it is, for the same throughput, a tank that has 2/3 more volume tends to take an efficiency loss of maybe 1%...on a 92% efficiency factor that works out to about 1/8th more standby losses. Sometimes it is 0% different. As near as I can tell looking at energy guides, the water output and energy usage is the same for these comparisons.
Volume is indeed what we are discussing and as you say, it is not of itself a standby loss factor. However, unlike you state, standby losses do not appear to be anywhere near 1:1 with surface area. Nice try, but you missed by a mile.
The smaller nonlinear aspects of near-tank plumbing only become apparent when you get to the very small sizes
Judging by efficiency factors they become apparent well before that. There is a reason that the efficiency factors don't trail off rapidly for a given insulation thickness when the tank size goes from 30 gal to 50 gal, or 40 to 80 gallons (looking at a State High Efficiency electric table for the latter...same 0.93 EF for both, with R20 insulation on both, roughly 40% more area on the 80 gallon.)
My point is that "going small" with the tank in-and-of itself does little for efficiency. Reducing the length of runs has benefits, that we agree on. One has to compensate for the lag time in long runs...or waste considerable energy. However, one has to weigh the expense and upkeep for the second system against this waste. If I was going to sell the second water heater in the kitchen end of the home, it would be for
convenience. And I would still insulate the tank and lines.