But such a scenario "would raise stability risks in Bangladesh," says Romen Bose, deputy head of Asia forecasting at IHS' Exclusive Analysis, an outfit that assesses political and violent risks worldwide.
"For the government to ban Jamaat would mean pushing them against the wall," with the potential for a guerrilla-style insurgency if the party is locked out of politics, he said.
Meanwhile, Jamaat's tactic has been to turn criticism of it into criticism of Islam.
Jamaat has called the Shahbag participants "anti-Islamic atheists" who deserve death for defaming the religion but who are protected by the government.
The party also accuses the protesters of seeking to overturn an independent judiciary.
On February 15, a blogger and one of the Shahbag organizers, Ahmed Rajib Haider, was hacked to death hours after he called for a boycott of Jamaat-affiliated institutions and businesses.
An atheist, he is alleged to have been behind anti-Islamic posts, which protesters contend are part of a cyber war to malign the movement.
So far, the Shahbag protesters and Jamaat supporters have not had direct confrontations -- a scenario Bose says would be "disastrous."
But increasingly, the Islamists are letting their presence known with larger and larger rallies and strikes first in cities outside Dhaka and then in the capital city.
On Friday, at least 18 journalists were attacked by Jamaat supporters after Friday prayers.
And on Sunday, several thousand Islamists took to the streets in Manikganj after an imam of a local mosque urged them to rally against bloggers he accused of insulting the Prophet Mohammed. Police fired nearly 300 gunshots and 50 tear-gas shells to disperse the mob.
Other Jamaat-led protests also turned violent. In all, 24 people have died so far, and Jamaat has called for a general strike Thursday.
To be fair, both sides are trying to muffle each other.
On Tuesday, Shahbag activists marched to the home ministry with a memorandum demanding the arrest of the editor of the newspaper Amar Desh for instigating violence with reports that their movement was anti-Islam.
The editor, Mahmudur Rahman, who is being sued for such charges, has been defended in the past by the Observatory for the Protection of Human Rights Defenders, citing "ongoing judicial harassment."
Amar Desh, according to the group, reports on corruption cases in Bangladesh.
More recently, the group expressed concerns about a restricting environment for human rights activities ahead of elections next year.
Photographer Shah Sazzad Hossein has gone to Shahbag about a dozen times to get a sense of who the demonstrators are and what keeps bringing them back.
He says he sees no signs of the rallies abating, with people wanting nothing less than the death penalty for war criminals.
And yet he cannot shake a feeling of foreboding.
"I think there will be violence in the coming months," he said.
Then he added, echoing the sentiment of the masses assembled in Shahbag, "I'm not afraid."