But this overlooks the fact that deep changes have taken place in Egypt since the 2011 revolution, changes that make such an approach potentially incendiary.
In Mr Mubarak's time Islamists were prevented from organising and practicing their faith in the manner of their choosing.
Since his overthrow, they have had the freedom to do what they choose and it is not going to be possible simply to turn the clock back and stuff the genie back in the bottle.
Furthermore, the forces behind the latest coup included salafis, sincere secular revolutionaries and members of the old regime, a strange mix of bedfellows who do not share much besides their hatred of the Muslim Brotherhood. They certainly will not be able to maintain a cohesive political front for long.
After a few weeks, General al-Sisi would likely founder trying to navigate Egypt's many problems. As we saw in the months immediately after the 2011 revolution, the army is inflexible and hopeless at politics.
The Muslim Brotherhood would play spoiler, mobilising its huge numbers of highly motivated supporters to paralyse the country through peaceful activism. They have deep roots in Egyptian society and public sympathy at how they have been treated is growing.
Many Egyptians who supported the coup are already having second thoughts now al-Sisi has been revealed as an unreconstructed military ruler just like his predecessors.
The roots of the situation Egypt now finds itself in can be traced back decades. Poverty, social inequality and unemployment proliferated under a succession of military dictators. In the final years of President Hosni Mubarak's reign, the corruption and looting by members of his inner circle accelerated.
By the time President Morsi became Egypt's first democratically elected president on 30 June 2012, the country had such deep social and economic problems it was already arguably ungovernable.
But rather than share this poisoned chalice with his political opponents, ex-president Morsi and the Brotherhood foolishly did all they could to consolidate power for themselves.
Their much touted economic plans turned out to be non-existent and the situation was further aggravated by acts of folly, such as appointing a governor of the major tourist attraction Luxor who had connections with a group responsible for murdering tourists there in the past – and then promptly un-appointing him.
In fact Mr Morsi was doing such a good job digging his own grave politically that if he had just been left to it for the remaining 3 years of his elected term he might even have destroyed the Muslim Brotherhood for good.
Ultimately it is the Egyptian people who can change the balance of power.
The Egyptian army is a people's army and so they are as influenced by Islamist thinking as everyone else in Egypt.
As in the Iranian revolution when the Shah thought he had control of the army until the day he discovered he didn't, the army could revolt or split, paving the way for either an Iranian style revolution or a Syrian style civil war.
Seeing what has happened elsewhere in the region, this might seem from afar like a likely outcome.
But one cause for optimism is that Egyptian society has an innate stability that differs from most other Arab countries and Egyptians generally have a highly peaceable and civilised nature.
Despite their differences the majority still have a deep belief in the unity and social fabric of the state, which is why despite being subject to intense social and economic pressures society has never broken down in Egypt as it has done elsewhere. One can only hope that stability holds during the current crisis.
: Hugh Miles is an author and journalist specialising in Egypt. He is the author of Playing Cards in Cairo.
