OK, for the sake of discussion, let's say that SHTF means no more propane - even though current propane storage would last for years -
SHTF = No utilities, no access to stores of any kind (no groceries, no gas stations, no clothing stores, no restaurants, etc.), no gasoline, no propane....all the luxuries we have enjoyed go bye bye.
Ok, so you will be stockpiling propane?
Do you know how much propane you would use in a day? How about the increased amount during the winter? How will you gain access to such storages of propane if they were accessible at all?
Also, how will you transport said propane from the storage location, they weigh quite a bit? Not to mention, how many others are you going to have to fight off going after the exact same thing? And last, do you believe you will be able to afford it?
and you have to fuel your water heater with wood.
And?
The water heater is just being used as a storage container, the stove does the heating. Not a big deal.
How much wood have you processed without the benefit of gasoline? Do you own a two-man felling saw, two-man crosscut saw, splitting wedge and have the time to make kindling as small as that in the photo in your OP? Do you have any idea how much wood you would use in a day? Do you also plan to use wood to heat with in the winter?
How many years was wood used before gases and such came along?
How many years was wood gathered before two-man saws and such came along?
I have cut down plenty of trees over the years with an axe (and yes, if need be an axe can be made in the home easily enough and so can a basic saw). Does a chainsaw make it easier, sure...but necessary it is not.
When you are supplying only wood for yourself/family and a small shelter, it doesn't take much to heat the place (also, if need be, gather everyone into a single room and you will be able to extend your resources). Also, using a rocket stove or other such efficient stoves, it doesn't take much wood to make a lot of heat.
An axe/hatchet/handsaw can easily produce the the kindling that size... in fact I did so just the other day, they don't have to be all perfectly straight or equal thicknesses, just small enough to fit several in there. Also, a good bayonet/kabar is great for splitting wood into smaller pieces.
All the same things you would do during the rest of the year you would still do during the winter. Now, of course, to ease the winter, it would be wise to have a large pile of wood on hand, which is easy enough to do.
People are way too dependent on technology, they can no longer see past it or doing anything without it. People survived many years without such unnecessary luxuries...
Hot water, for bathing or washing clothes or dishes, can easily be produced by putting a pot on top of the wood heating stove while heating your home during the winter.
Yes, it can as recognized earlier, would it be as quick or efficient...no it wouldn't. But the rest of the year do you really want that wood stove running? Winter sure, it's already running, but the rest of the year it would smother you out of the house/shelter.
Solar is OK, but - unless you utilize it to produce electricity to power an electric water heater - isn't going to produce particularly hot water. Anyone who's ever owned an electric water heater knows how (in)efficient that is.
Sure, solar won't make the hottest water, but it will be hot enough to bath comfortably in and clean things...and as recognized, has it's limitations as heating stops at night and has to start all over the next morning, plus you have account for ambient temperatures.
Solar electricity...great as it is, not able to build in your home and also limited during winter/overcast days.
So, yes, a combo system. Solar Water Heater for use during the day (late spring through early fall) and a wood stove water heater for night and the winter.
In-line propane-powered water heaters are exceptionally efficient.
No one said they weren't, but you are still dependent on the "grid" (or would you rather the word "system" be used instead?) and others providing you resources.