what you are missing is that the behaviour you set in the example is not investor behaviour, but rather trader behaviour. naturally it is best to buy when the price is low and exchange rate is high, and best to sell when the price is high and the exchange rate low but these are the extremes which rarely if ever occur in reality.
The typical investor approach is not to put too much weight on a single transaction. since the plan is to hold the shares and not actually sell them over time, you will find each addition to a position will have its own FX rate and share price. after 2+ years in a stock, your average FX rate will see little fluctuation from short-term erratic behaviour. perhaps you don’t get as much now as you could have in the past or future additions, but now is when you have the money.
you could hold off and instead better spend the money in a local company so as to avoid a bad FX rate and make a deposit to a foreign company when and if the rates turn back in your favour a little on a later date which you cant guarantee. at least today its 1.15 tomorrow it could go to 1.1 and never again reach 1.15 for the next 50 years (extreme but possible in theory) after all, the FX rate used to sit comfortably above 1.5, and for a while had gone as far as 2
a calculation you forgot to do is “what if the Rate drops to 1 or 1.1” once you have an open position in a foreign currency, a drop in fx rate could see you making a tidy profit even if you sell the shares for the same or less than you bought.
I have positions in O and PEP. I will not be selling these shares in the next 10 years, over those 10 years I can expect the FX rate to change, some days they will be a better deal than others, and instead of averaging monthly I could opt to only buy on the few days where I see favourable prices, but ultimately I will not sell these shares. if the FX rate increases, my next purchase will get me more for my money, if the FX rate decreases my position becomes worth more in my local currency. as far as I am concerned, that’s a win-win in my books.
final note: buying foreign shares is a calculation of FX rate x share price. when the FX rate sees a violent adjustment like what is happening now, you will often see company share prices have also been affected by the news to a varying degree according to sector and industry impact. so even though I cant get as many for my £ right now, I can buy shares for less than I can normally. this means the value of the share evens out and I need only compare whether I am ultimately paying more or less than normal for a single share in my local currency, not in the shares native currency.