Para 1) Applies to cars, but over a shorter timeframe, and I have previously explained why including cars in the current form is also wrong (but could be justified if the methodology is adjusted through partial inclusion in a basket)
Why should the timeframe frequency of purchase for the individual matter. I would say what matters is that you can measure the price of houses (which is already done) and if the price of those houses is is increasing/decreasing as people buy them. Why does it matter that the person buying the house today is not the same person who is buying a house tomorrow?
Furthermore, there are many things in the CPI basket that very few people buy, electric bikes are in there for example.
Para 2) Not just the fact that people rent, most buyers "pay" via a monthly financing arrangement such as a mortgage, and it is the variability of the monthly payment that should be captured as the consumption cost, and the change in the cost of living within an inflation figure. Over much of the last 20 years house prices have risen but mortgage payments have fallen. What is right about including the rising house prices when consumer inflation for housing consumption has been lower monthly/annual prices?
So, many people buy cars and other things on finance and yet cars (and others) are in CPI as said before.
What you appear to be arguing for here is that because the cost of credit has reduced and thereby the monthly cost of servicing that debt has reduced for the consumer, we should ignore the initial price of the item that the credit has been obtained for.
The problem with this is that you seem to be forgetting that most mortgages require a deposit, the size of this deposit is often directly Impacted by the price of the house and thereby this also impacts how much money the buyer needs to save to be able to raise it, this has a direct impact on the buyers cost of living and even their ability to purchase the house entirely.
For this reason alone I can’t see how it can be argued to include the cost of credit and exclude the price of the house.
But more importantly, (and this is the reason where I would’ve thought the BOE would really want to include house prices at is directly impacts their price stability mandate ), by not including house prices in a cheap credit environment, a bubble has been allowed to develop which now, when credit is less cheap, is going to result in a far
More challenging economic and political environment for the BOE/government to manage than it otherwise would’ve done had house prices been included.
Your final paragraph has a lot of merit. Which again leads me to conclude your actual belief is the MPC is using either the wrong tool, or combination of tools, and should be addressing additional factors when considering monetary policy. Nothing I haven't said already but crucially this isn't the issue with CPI (or inflation generally) but something else. Any reason you care not to express that itself rather than make claims that CPI's non inclusion of assets is a problem?
That’s a fair question and I guess that my argument is that house prices (not just the cost of finance or the cost of running a house) should be one of the things that’s included by the MPC when they are measuring inflation and thereby making their decisions on what to set the base rate to. It doesn’t necessarily have to be CPI if another approach achieves this goal