This 1992 book suggests that volume metering (ie, simply measuring and charging based the volume of hot water delivered to an end-user) may be superior to energy metering (ie, measuring the actual amount of heat delivered) for geothermal district heat systems. Wikipedia makes a similar suggestion, generalized to all district heat systems, but doesn't offer a citation for it. In both cases, the argument seems to be that energy or heat measuring is more complicated, expensive, and error prone, and that volume metering has the added benefit of incentivizing the end-user to more efficiently extract heat from the hot water they receive.
However, my impressions is that energy metering is much more common than simple volume metering. The 1992 book mentions that the majority of geothermal systems use energy metering, and more modern sources seem to take for granted that heat meters are integral components of any district heating system.
The above two sources are the only ones I can find that actively compare the tradeoffs of volume versus energy metering, and obviously neither is particularly detailed, authoritative, or up to date. My impression is that energy metering is generally preferred for modern systems, yet I cannot find any good sources that explicitly argue for this preference.
What are the advantages of energy metering over volume metering for district heat systems? At this point, is there a clear preference, or are both still considered for new systems?