"What generally happens with such cases is, if you plead guilty to the speeding offence, the fail ID driver offence is then withdrawn and the court would sentence you on the speeding offence."
That is called "laying the charges in the alternative". Some courts have taken to formally doing just that. They say - in writing - that the two are alternative charges and that if a guilty plea to one is made, the other is dropped. It is a sensible way to proceed because without a guilty plea, both charges cannot succeed. However, they are not truly alternative charges unlike, for example, dangerous or careless driving. In those circumstances there was only one offence committed (bad driving) and it's just a question of how bad it was. A driver cannot be convicted of both dangerous and careless driving arising from a single incident.
In your case there are two distinct offences, one committed long after the other, and in theory you could be convicted of both. You have nothing in the way of a defence to the FtP charge and would almost certainly be convicted of it in the event of a trial. But if you plead guilty to speeding as well, the police do not need the evidence that you have failed to provide (i.e. that you were the driver) and you could be convicted of that as well.
Although that is unlikely to happen, based on what you have been told ("...
What generally happens...") it remains a possibility. I am surprised that the court has not simply accepted your offer. I would be reluctant to plead guilty to speeding until you have a guarantee that the FtP charge will be dropped.
"What generally happens" as explained by a member of the court's admin staff is not such a guarantee.
I would respond by saying that a guilty plea to speeding is conditional on the FtP charge being dropped. If that guarantee can be provided in writing you will change your plea. It's unwise to rely on what court admin staff tell you.