While I can't speak for all coups, the junta era of Latin America featured a number of military coups, some of which lead to democracy. Most 'revolutionary junta' governments of the era viewed themselves as temporary dictators (a la Cincinnatus) who proclaimed themselves a purifying force on society and government, with the explicitly stated goals of holding free and fair elections at a later date. 'Junta' in Spanish simply means "council" or "board" and does not have the same connotation that it does in English.

Of course, this is complicated by the fact that many of those elections were not actually free and fair, and the fact that many of these juntas were declared in an effort to nullify the results of a previous election. The lack of legitimacy definitely led to long-term problems of government, and especially a dependence on military power as a method of ensuring cooperation with the broader population and additionally opened up the door for other factions to declare the new junta illegitimate because they lacked democratic endorsement.

Overall, it can safely be concluded that military coups are not conducive to free speech, democracy, and representative governments. However, representative democratic governments have emerged peacefully (or semi-peacefully) from military coups in the past (i.e., all is not hopeless). The late 1980s-2000s witnessed the "Retreat to the Barracks" Phenomenon throughout Latin America, in which many military governments relinquished power to civilian governments.

The reason for the 'Retreat' seems peculiar through the Machiavellian lens of power politics, but several things must be considered. First, the Cold War dogma in the US of always supporting autocrats because autocrats would keep out the communists, was receding, thus knocking out a key pillar of support to many military regimes in Latin America. Second, there appeared to be a a rise of the acknowledgement of the limitations of government which occurred in parallel with the rise of neoliberalism (using the term broadly). Thus, many of these regimes grew frustrated with governing and their lack of ability to magically make society "better" and the economy larger through government dictates and military-like operations. Third, and most importantly, the marginalized, which included the large majority of society under many of these regimes, organized, resisted, threatened violence or stern non-violent resistance, etc., and won!

Sources:

Faces of Latin America by Duncan Green and Sue Branford - great overview of modern and contemporary Latin America

Inevitable Revolutions by Walter LaFeber - a 'revisionist' history of Central America during the Cold War/Junta Era, with discussions of legitimacy and the nature of junta governments dependent on foreign support.

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Also which may be of interest is the historic, seemingly paradoxical role of the Turkish Military in ensuring secular democracy in Turkey, but I cannot speak to the topic as well as others.