don't shoot the messenger, I did not write BS 7671. As said "may" need three wires, it would depend on the control voltage of the boiler, if extra low voltage like 24 volt or 48 volt then no not required, same as there is no RCD protection for the door bell wires. But if switching 230 volt then yes, must run earth, even if not used.
I would assume rule was so when items changed from class II to class I the earth is available. It also stops being able to use the green/yellow wire in three core flex for line when fitting a tank thermostat, as the earth needs running anyway, so if three wires required need to use 4 core.
Oddly when wiring a boiler to a wiring centre with more than one cable one can technically use one of the green/yellows and over-sleeve, I think bad practice, but the regulations can be read as only no permitting it with singles.
I would agree does seem a bit daft, if the thermostat cable is not fixed and can be plugged in, it would be an appliance not part of the installation so you can get away without the earth. Use one cable clip, and it becomes installed, and swaps from being inspected with the PAT testing to being tested with the EICR.
And it is the EICR which has become a problem, mainly with rented property in England, things missed for years are raising their head, although the EICR looks for danger and potential danger code 4 which was does not comply with current edition was removed, and I would not code using two core rather than three core to the thermostat.
However the Emma Shaw case
points out the problems when the earth loop impedance is not tested correctly, today with RCD protection that could not happen, but the earth rule came in 1966, and the RCD to nearly all circuits came in 2008. There was when the RCD came in also a relaxing of bonding rules in bathrooms, but not running of an earth to each point even if not used.
The rules do cause problems, as not retrospective, so you can still have a home without RCD protection, but as soon as you start to do work, it becomes a requirement. It was you who pointed out to me how Worcester Bosch with some boilers not only state RCD protection but also that it must be type A not type AC. It no longer says we must follow manufacturers instructions, we need only to take them into consideration, but on fitting a new boiler one needs to complete and sign the minor works certificate and one needs to be brave not to follow manufacturers instructions.
Yes I would agree the regulations seem some times to rule our lives, when in around 1992 I returned to UK, all we seemed to hear was the 16th edition says this or that, when I left UK in 1980 no one seemed to worry about the regulations, it was when the regulations became a British Standard (BS7671) when it seemed over night people were tested on their knowledge of the regulations and we started to follow them it seemed to the letter. Although not quite as strictly as gas people followed their regulations, I have seen gas men refuse to fit a cooker as the wall units are ½ inch too low.