Maybe, but around me, house demand hugely outstrips supply, so everyone buys at the limit of what they can afford. For sure, proper dumps that need significant renovation go for less, but they are super rare. Everything else goes for a price set by the size of the home and increasingly, the size of garden. New builds command a slight premium, but that's mostly a marketing premium, which doesn't hold for resale. It's hugely complicated by the location aspect of course - older houses tend to be in better locations. Basically, my point is that trying to attribute regulatory costs to house prices is essentially impossible, and is very much in the noise.

Not to argue, but rather to add my experience as it is fairly unique, I did a renovation to a property that cost a low six-figure amount of money (£).

Few have done this so whenever this conversation happens everybody talks about house prices as if there is nothing driving them other than "planning permission is an expensive, time-costly and risky endeavour" -- that's not all as the cost of doing building work is very high! While there were a range of build costs given to us by building contractors, they were all eye-wateringly expensive and at the lower end you have to carefully consider the risk of fraud.

Overall we had a very painful experience and the project was beset with poorly executed work and fraud until we realised what was happening half-way through the project and diverted a large amount of our resources into sorting everything out [0]. As a professional software engineer, I'm used to being able to trust that people will do what they say, but this market is a whole different game and much more cutthroat. We specified exactly the work that should be done and the materials that should be used with an architect's help but this isn't enough: you have to carefully evaluate every single piece of work to ensure compliance and be ready for gamesmanship/fraud or even financial/legal conflict from contractors.

My point is that house prices must reflect the the costs/risks of building and these are numerous:

  - Designing, quantifying and specifying work 
  - Navigating bureaucracy and failure to get sign-off
    causing costly re-designs
  - On-site supervision of workers completion of jobs and
    assessment of materials used
  - Evaluations of work completed by independent surveyors
  - Organisational and project management skill
  - Understanding of construction and contract law with its
    many peculiarities (e.g. were you aware that you must pay
    *any* amount that a building contractor specifies in a 
    validly constructed payment notice unless you have sent 
    a pay less notice with calculations showing otherwise? 
    This is often used in "Smash and Grab" abjudications to
    force clients to pay money as "if the paying party does
    not serve the right notice against your application then
    they must pay first and argue later." [1])

There aren't as many skilled tradespeople as there used to be and quality building work is labour/skill intensive, complex and risky. My experiences leads me to believe that the lack of competition between contractors is just as likely to be driving high house prices as overall planning risks/costs. (It's just that the former is opaque and invisible to most people even if they work in research/policy.)

  [0] Our contractor went as far as attempting to extort money from us by getting a subcontractor to send threats to us and finally slinked away unscathed once we involved a quantity surveyor and lawyer.
  [1] https://helix-law.co.uk/smash-and-grab-adjudication-overview/

We went through a similarly priced renovation. We had a different objective to many doing similar to us, which was to improve the energy efficiency of the house. It was interesting to see how incompetent the tradespeople were when the requirements deviated slightly from the norm. We had the usual shenanigans of course: the electricians gave us a bill that included a huge amount for materials, so we asked for a breakdown and found that they'd charged for hundreds of meters of cable that I could prove were not installed (impedance measurements gave me a good upper bound on the total installed length). I simply refused to pay more than a nominal amount until I was given an accurate bill with evidence, which never came (I suspect it wasn't malicious, it was just each electrician buying a reel of cable and chucking the remainder in their van for future use).

I also got into quite a heated argument with a plumber about static vs dynamic pressure and flow rates (it turns out fluid dynamics is not really part of a plumber's training).