Morsi was chosen by the majority in a democratic election. The June protests included supporters on one side and the opposition on the other. With lack of accuracy about what side outnumbered the other, the Military coup was not justified in siding with the opposition. This position led to violent confrontations between the Military and the Morsi supporters. The arrests (without trial) and shut down of TV channels will only worsen the chaotic situation in the country.
Instead of a democracy, Egypt will have rule of the mob leading to an endless cycle of violence and protests, possibly a Civil war. US support of a democratic system in Egypt will maintain US credibility and contribute to region stability.