The premiers of the country's 16 federal states, which comprise the upper house of parliament, on Thursday voted unanimously to outlaw the the far-right party despite concerns it could fail like an effort in 2003.
Funke said a successful ban and the consistent and decisive prosecution of neo-Nazis would be a fitting response to the shocking racist murders of nine people across Germany by the so-called National Socialist Underground (NSU), a neo-Nazi terror gang.
"It would a legacy that would show respect to the victims and their families - it would be a suitable reaction," said Funke, a professor at Berlin's Free University Otto Suhr Institute of Political Science.
It would also force the police and intelligence services to crack down on far-right violence and intimidation, he said.
Only Germany's Constitutional Court has the power to ban a political party - and it requires an application from either the upper or lower house of parliament, or the government to consider the idea. That application must be backed with legal arguments and proof to show that a party is aggressively working against the constitution.
"It is possible but it depends on making the proposal carefully and this is where the real work will be needed. They have to ensure that the material submitted is free of influence from informants," he said.
The 2003 attempt to ban the NPD failed when it emerged that undercover informants for the intelligence services were behind much of the evidence showing the party was anti-constitutional.
Careful checks to restore credibility
Funke said any submission for a ban should only be made once an independent investigator had checked the files for any hint of informant involvement. This could be a way for the police and intelligence agencies to restore their badly damaged credibility in the eyes of the court, he suggested.
"The Constitutional Court might not believe the submission was clean of informants, but an independent investigation could help to clear that up," he said.
The NPD was, he said, a neo-Nazi organisation, acting as the political arm of groups some of which had already been banned for outright for violence and outright fascism.
"Some liberals want to have the party out in the open, and of course that is a reasonable argument. But there is a problem with that - I think even in comparison to other West European democracies - a big problem: We have about 1,000 violent attacks a year, at least. We have 13,000 active and potentially violent neo-Nazis, and this continues."
He said there was a direct link between the NPD and aggressive neo-Nazis who attack or intimidate people on the bus or in the street. "It feeds them ideologically and gives them a sense of legitimacy.
"These violent guys or the gang use this party - they join and then leave again depending on circumstances. And although the party says that de jure there is no link, de facto there is."
A ban to force the police to act
And not only does the fig-leaf of legitimacy need to be removed from the NPD's supporters, Funke said just as important was that banning the party would force the police and security services to take the subject seriously.
"There is a playing down and denial of the problem, like you saw with many people [from the authorities] giving evidence to the commission of inquiry into the NSU attacks. People were saying it wasn't their problem, and that the real danger was presented by Islamists - and before that they were focussing on the [left-wing terror group active in the 1970s and 1980s] RAF."
He said this was demonstrated by the statement of Kurt Biedenkopf, the former state premier of Saxony who once said Saxons were "immune to right-wing extremism."
And the police and intelligence services needed to be shaken awake and forced to take the problem seriously. "They are not in good shape, we have seen that," he said, referring to the catalogue of serious errors of practice and judgement made across many security services during the years that the NSU terror gang were committing racial murders.
A decisive move was needed to force German democratic forces to be strong enough to deal with the problem of right wing extremism, he said.
"This is the first chance we have had since reunification to ban the party, and we need to stop that racist, anti-Semitic shit," he said.