It's certainly true that smart meters are more accurate than the old ones, but it's not always the case that the old ones under-read, at least not without outside interference. The big problem with the old meters were that they couldn't provide readings with the frequency necessary to enable suppliers to offer time of use tariffs, and also because the old meters were easily nobbled either magnetically or physically.
The core strategy of the electricity industry is to try and get people to shift their electricity consumption to even out demands on the grid, with some suppliers offering negative electricity pricing (ie they pay you to use it) at certain times in return for higher costs at peak times. Nearly everyone offers an EV owners tariff giving ultra-cheap charging between midnight and 5:00AM.
Resistance to having a smart meter is quite widespread in some demographics and I wonder sometimes if people are aware that they are condemning themselves to higher electricity prices than they might otherwise be able to get away with.