I'm feeling it's kind of a question of: Okay, at what point do you throw out the rulebook and do what works? You can't please everyone. There was a popular revolt of sorts. Would we like the military more if they 'kept to their role in an advanced democratic society,' obeyed their chain of civilian command and -- as a direct result -- attacked the majority on the streets set against having Morsi? I don't think so.
Meanwhile back in the oh so balanced USA: In retrospect, sure, our lovely due process has finally gotten around to declaring that the police who defended the 2004 Republican National Convention did all sorts of unconstitutional stuff on the streets in defense of an unpopular administration. It only takes them 2-5 years to sort out the various cases, and a lot of help that is while people are being searched and detained by the hundreds for a week... Now multiply that by all the powers Morsi was handing to the fundamentalists in Egypt, for all the months and years he would be in power. The only difference was: he was going to have his people rewrite the constitution to "justify" it, operating by themselves after he promised to let other factions into the process.
There's another problem that the society may be so politically strained by circumstances and fragmented, that nothing may work especially well for the foreseeable future. Although in that case, the military could argue once again: At least we attempted to stabilize the situation as best we could. Now if the Muslim Brotherhood comes out swinging against the next regime, is that any more democratic really than what the military has done?
For a messy analogy but one I like... If Obama had the guts to put say, the Senate filibuster rules up to a popular vote for a constitutional amendment... Even though that would be done through due process (possibly taking his whole first term to accomplish!), and even though that would have been reinstituting the same structure the US previously had as the legislative process, with fewer Senate votes required to pass laws... I bet there would be quite a few people in the streets complaining that he had broken the rules for his own benefit.
So: You can follow the rules to get things done in a crisis, if you prefer -- possibly doing it all too late that way to serve the people who elected you to do something promptly... and regardless quite a few people will shout foul and promise secession, retribution, disbodience, on and on. Heck we haven't gone that far under Obama, less has been actually done because of Congressional gridlock mainly via the fillibuster, and still look at how politicians particularly from the American South rant on about "abuse of power" now.
At least as I gather from brief views on CNN: Morsi, however, made a rather bald-faced power grab that also redid the constitution and in the process quite clearly lost his popular majority. Or if not?? Then, I haven't heard a well-supported denial , yet.