But while most of the National of Union Teachers' 314,000 members would relish an end to the mindless militancy of the Easter conferences, large numbers of the 253,000 National Association of Schoolmasters/Union of Women Teachers and 187,000 Association of Teachers & Lecturers members fear merger because of such extremism.
And perhaps surprisingly, given the support within the ATL leadership for unity, a poll in April found nearly half its members oppose a merger, compared to 30% of their NAS/UWT colleagues.
However, Peter Smith, the ATL general secretary had an easier ride at his annual conference than his newly appointed opposite number at the NAS/UWT, Eamonn O'Kane. Mr O'Kane had started the debate after taking over the union leadership from Nigel de Gruchy, who had long been an opponent of a merger.
Meanwhile the 40,000 strong National Association of Head Teachers and the 10,000 member Secondary Heads Association present a divided front among school leaders. Even if the big three merge, there could still be four teaching associations in England.
Unions already have de facto unity over pay submissions and teacher workload. On issues where there were conflicting views, such as special needs and discipline, the National Union of Teachers and NAS/UWT have moved closer on policy.
And there are big changes afoot in the classroom, with the growing use of paraprofessionals and new technology. Broadband technology will, for example, offer the chance for many more specialist lessons to be delivered remotely.
So it would certainly make sense for teachers to have a single voice. And a union of over 500,000 serving teachers would be hard for ministers to ignore. Its members might also hope that economies of scale could greatly improve the services provided, which lag far behind those offered by their American cousins.
Ministers may welcome a single union, too. Beyond the prosaic business of cutting down on meetings and Easter conferences, it could help them to get their message across better.
There are those who argue that a divide-and-rule approach served the government well on issues like performance related pay. It did not. It delayed decision-making, confused teachers and ensured that the difference which PRP made to teachers' salaries was obscured from new recruits.
And while a single union strike could cause maximum disruption, it would be less likely over minor issues. Once it backed reforms, ministers could hope to introduce them effectively
A merger will not be easy. Yet other unions have overcome such obstacles. And the teaching unions will merge eventually. Whether it happens more quickly depends on the resolve of three general secretaries who are keener on unity than any of their predecessors.
Special adviser (1997-2002) to former education secretary David Blunkett