Terry Motau SC, for the municipality, also argued that there was no proof that anyone had been harmed by the name changes,
The municipality has applied for leave to appeal against an interim court order, granted in April, interdicting it from removing old street names and ordering it to re-install old signs which have already been removed.
The order was granted pending the final outcome of civil rights group AfriForum's application to set aside Tshwane's March 2012 resolution to change the "offensive" names of 25 streets.
AfriForum is involved in a protracted legal battle with the municipality about replacing the name Pretoria with that of Tshwane.
Some of the city's oldest street names disappeared overnight when Tshwane's undertaking not to remove the old street names lapsed in October.
The city argued that the application should not have been heard as an urgent matter because AfriForum waited five months after the six-month period lapsed to launch the application.
Motau argued that the interdict intruded into the exclusive terrain of the city.
"To restrain the city from implementing its resolution would be to intrude into its domain, the "heartland" of its functions," he said.
He argued that AfriForum had "alarmingly and glaringly" failed to prove that it would suffer any harm at all, let alone irreparable harm.
"It's a matter of national importance. It's not just a simple interdict that was granted.
"AfriForum relied on a cultural right and fair and just administrative action.
"The court erred in finding there's a right that's being infringed.
"The mere changing of a street name cannot breach a right to culture.
"You can't engage a right in the abstract. You have to show how the process infringes a right.
"What is cultural about changing a street name from Vermeulen to Madiba?" Motau said.
He argued that the court had erred in ordering that the street names already removed be reinstalled, especially in circumstances where there was evidence that the reinstallation would cost the city about R2.6m.
"The proverbial horse has already bolted. You can't unscramble the egg.
"An interdict is forward-looking. It is unsuitable to remedy a past, non-continuing harm," Motau argued.
MP van der Merwe, for AfriForum, said an interim interdict was not appealable.
"What can ever be harmful to restoring those well-known, respected names that had been there for decades? At least no one will be lost," he said.
Van der Merwe said the city had only itself to blame if it had to spend over R2m to put the names back.
The city had started taking the names down while a review was pending and did exactly what the interdict was trying to prevent two days before its undertaking lapsed.
"We're not dealing with the city council of Pofadder and there's no suggestion that the city cannot afford R2m, even if it is a huge amount," he said.
Judge Bill Prinsloo will give a ruling on the application on Thursday.