Yes, I think I see where now you're coming from. You have a concern that people will be misled by marketing, and will make what is first and foremost a financial decision based on innacurate information.
Exactly - inaccurate information and/or misguided assumptions.
In fact, it's quite a similar situation to that in nearly all of my professional life (in fields very far divorced from anything electrical, or anything we discuss here). The end-result of matters I'm involved with is usually a decision, often relating to 'countless millions' and/or potentially the safety/wellbeing of countless people, but I never make the decision. I simply present the 'facts and figures' (and their implications etc.) relating to one aspect of the matter, and it is then for "them" to put my input, together with other considerations that have to be taken into account, into the melting pot which they use as a basis for their decision.
Just as I may explain to people what decision I made about PV in my own house, and why, I will often say to a client "if it were me who had to make the decision, then I would be inclined to ....." but that is just another thing which goes into their melting pot - and not something I can even do/say if there are major 'other considerations' which I am not able/competent to take into account.
I have a different concern, which is that people will make a decision about how they spend their money, based on the false assumption that they must firstly not spend it in a way which might leave them less than they started with in the short term.
For a large proportion of expenditure ('purchases') it's more than just the short-term. Ignoring complications like inflation, if one spends £XYZ on a purchase, then one will be worse off by £XYZ for the rest of one's life as compared with the situation if one had not made the purchase, and it's as simple as that.
With other things (like PV, 'maintenance', insurance etc.) it's more complicated, since the financial 'loss' will not, or may not, last for ever and, indeed (e.g. in the case of 'maintenance' and insurance), may have the (financially) 'positive' effect of eliminating major financial losses in the future.
It is in these situations that one needs a good understanding of 'the estimated arithmetic' in order to make decisions, albeit they are often not easy decisions because they are inevitably at least partially probabilistic in nature. In some situations, appreciable 'short-term' expenditure on maintenance/insurance may not be considered 'sensible' in relation to the possible cost of replacement of the item at some point in the future.
PV is a bit more straightforward, in that there are less uncertainties - the main ones being about future energy prices and the (post-warranty) longevity of the PV installation. If energy prices remain unchanged and the PV installations lasts way beyond its warrant period, then it's easy enough to estimate the (inevitable) 'cost savings' which will start to be enjoyed in X years time. However, it needs to be remembered that 'things change', and that the eventual 'cost savings' that we estimate today are probably nearly double what we would have estimated just a year or so ago - and we don't know what further changes there will be in the future.
The assumption about the primacy of short term avoidance of financial shortfall is embedded in your responses, and subtly but powerfully reinforces the beliefs that we ought to put 'taking care of myself financially, in the short term' above other considerations, in a way in which we don't for other home improvements.
I do understand that this may be the assumption you used for your decision re solar PV.
It's not really 'my assumption'. As I've said, it's a matter of individuals making a decision (as 'well-informed' as possible) on the basis of comparing the probable situation (over time) with and without the PV installation - and that decision will (based on the same 'facts') vary considerably between individuals, particular is relation to individual attitudes to 'risk taking' in relation to the areas where there I uncertainty. Some people are very risk-averse, and hence would not want to discount the (very low probability) possibility that a PV installation might have to be replaced "the day after it's warranty expired" - in which case their view of the arithmetic would probably be very different.
So my concern is that there may be many people who want to install a shed or update their kitchen, and feel able to do so, knowing full well that it's going to cost them money, and want to install batteries or ASHP or PV and the like, but don't feel able to because they believe that they must not or should not do so if it's going to cost them money in the short term. I think it's a shame if they miss out on doing what they want, based on this false assumption, which gets slipped in so invisibly - so it seems wise to point out its existence.
It would, indeed, be a shame if they were to make such a decision based on 'false' assumptions/beliefs/whatever - which is why I feel that they should be as fully informed as possible - and that includes them being helped, if necessary, to 'fully understand' the maths, as well as seeing it.
In fact, in the case of PV, the situation is often almost the opposite of what you are suggesting, since (usually as a result of marketing stuff) people have often come to ignore the short-term costs and think only about the potential 'cost savings' a number of years down the road.
When people start talking/asking about PV, it is very common (again, probably due to marketing) for them to start by talking about "pays for itself in X years". However, if I ask them whether they have considered that this means that they will be 'out of pocket' for the first X years, many of them say that "they had not thought of it like that".
Similarly, if I ask them if they have considered the fact that since the warranty is only for 7 (or 10, or whatever) years, that it is not impossible (albeit probably unlikely) that they would have to bear the cost of replacing the installation fairly soon after they had started enjoying 'cost savings', they very often say that they "had not thought of that possibility" My intention in asking them those questions is not to bias their decision but, rather, to make sure that they did take into consideration this things "which they had not previously thought about".
...and of course, if people do want to make a purely financial decision, then I agree that it's worth getting the maths guesses as accurate as reasonably possible.
Indeed. I would say that (in all the situations I've mentioned, including my 'day job' work'), no matter how many other considerations have to go into the decision-making melting pot, the starting point should be mathematical estimates which are as accurate (and based on realistic assumptions) as possible.
Kind Regards, John