Paul

The meters dont offer cheaper rates, they just record the usage across two counters (registers) - switching between them at different times of the day.

Your supplier can either charge different rates for the two registers, or the same rate.
That switch between registers is what will stop, the meters will carry on working, just logging all usage on one register.
So for most people, all they need to do is charge the same rate for both, and it'll work fine, as one will always have 0 usage.
Of course, if they still want dual rate tarrifs, they will need to get a new meter, but thats a choice, not a requirement.

However, there is an actual issue with a minority of these meters, in that some of them actually control the power to peoples heating and/or hot water, only powering them up on the 2nd (usually cheaper) rate. Those meters (and households) will have an issue, since when they stop switching, your heating/water will no longer power up (or be always powered up, but thats less likely). They are the ones that actually do need to be swapped, and should be prioritised.