I am wondering if we are speaking different terms here.
A demand meter is not always related to different billing rates but obviously has the ability to record highest rates of consumption.
In areas with flat billing or tiered rates the demand is a record of highest peak loading. This number can give you the spare capacity of your service equipment to add load a code calculation would not allow.
How often do we install a big service in a building only to discover that there was never a day where the service was loaded even close to its rating. With demand records it is possible to add load to the recorded demand.
For example you have an 800 amp service and the code calculations shows there is no spare capacity to say add a swimming pool heater or hot tub or another suite etc. You go to the utility and ask for the peak demand over the past 12 months and discover that the service was never loaded beyond say 400 amps so you discover the service has a spare 240 amps of unused capacity. (80% of 800 is 640 amps continuous load capacity)
The other meter type for flat rate billing is a consumption meter. They just record usage but never the peaks or valleys. You get a bill for kilowatts used over time but you would never know if it was used in 3 days or over the month. Sure you know the meter is read on date 1 and on date 2 and the difference is what you used but you were home for only 6 days with the heat on high and guests in the house. the other 24 days you were in Hawaii with the heat on low and the water tank shut off etc. The meter justs spins fast when you were home and barely moves when you were away. The bill just says X kilowatts over the billing period not when you used it and not the peak consumption.
So Demand meters just have a feature to record the peak. old mechanical meters had a red dial that got pushed every peak until it records the highest peak and the needle just sits there until the meter reader resets it.
Then there are the meters that record usage and time of consumption to match to variable rates. These meters record demand and consumption.
In the case of the hairdresser if the local rates are flat the demand meter won't matter but the consumption might show he is using more electricity a month than he is paying for. I know if I was the landlord I would install meters on each tenant regardless of rate structure and I would want a demand meter on the service in case I had spare capacity in the service that could be exploited.