I’m going to talk about the site I’m familiar with, old town Salvador, Brazil. This is really only the single area of the city that could be called “colonial.” The rest of the city is dominated by 20th and 21st century architecture.

It the original settlement built straddling a cliff face, originally wrapped by forts controlling the small port. It’s the perfect place to build a small fortified seaport, easily defensible. It was quickly built up. However as soon as the region was pacified and the danger of foreign invasion passed it became the least convenient neighborhood to be in. After all who wants to trudge up and down an escarpment every day? So aside from some core government functions, mostly the city relocated to more convenient sites, in the 18th century the city expanded this along the bay as the neighborhoods from Ribeira to Barra developed. In the 19th century this moved across the peninsula as Pituba and the modern downtown exists. The Pelourinho and the rest of the old city was largely abandoned by the middle and upper classes.

Despite this, the old colonial neighborhood saw continuous construction. Several of the key buildings were renovated and or replaced throughout the centuries. A lot of we think of as “colonial” architecture is nothing of the sort. The Palácio Rio Branco is from 1919 (replacing the old governor’s palace). The current Elevador Lacerda is from 1930. Praça Visconde de Cayrú was redone in the 1860s. So the area was not at all static, nor was anyone trying to preserve it.

In 1933 in a renewal project the Igreja da Sé was demolished along with a number of other blocks, resulting in the first series of debates in Brazil over historical preservation. In 1937 the federal government passed Decree-Law 25/1937 Instituto do Patrimônio Histórico e Artístico Nacional (National Institute of Historical and Artistic Heritage – IPHAN) and providing the initial protection for the neighborhood. The restoration of a colonial character wasn’t seriously considered until the 1980s and 1990s when governors João Durval Carneiro and Antônio Carlos Magalhães pushed for first UNESCO recognition and funding and then the restoration of the city to its historical roots. Some 1350 buildings were restored to a colonial character, many of which hadn’t been colonial, but were retrofitted to be colonial.

The whole area is part restoration and part creative recreation. And it’s largely out of keeping with the bulk of the city which has never tried to maintain a colonial character at all. And the only reason it was around for preservation in the first place is because it was considered an undesirable neighborhood from about the 17th century on. Basically it was preserved out of neglect.

This is more an architecture, urban planning and sociological related question than an historical one, but, actually there are plenty of fully preserved colonial towns in New England. Some of them dating from way before the Latin American cities you used as an example (perhaps not Cartagena, which would be older).

Here is a brief list with some current preserved Colonial towns in New England only.

But the main reason why you would see more preserved colonial sites in Brazil and Colombia, and other Latin American countries (and even in former British colonies in the Caribbean, as you stated), would be the way the United States transitioned from a couple of British colonies, in the end of the 18th century, to become the World's main economic superpower by the end of the 19th century.

So, in less than 100 years America come from nothing to become the main economy in the world (the translation of this economic power in political power would come later, with the two World Wars). American cities developed quite rapidly, in a surely breakneck way, while Brazil and Colombia remained underdeveloped and backward places, with no noticeable economic expansion or modernization, with those countries basically transitioning from their respective metropolitan powers (Portugal and Spain) spheres of control and influence, to Britain's sphere, and finally to the United States political and economic control sphere, where they remain even today.

As America needed to develop faster and faster, preservation of colonial cities and settlements became a secondary (or non-existent) thought held to the back of local government officers' minds, when confronted with the needs of providing working-class housing, electrification, building transportation networks, connecting industrial neighborhoods to the main cities, and so on, so forth.

Brazil and Colombia only experienced some real industrial development by middle 20th century, when historical preservation had already become part of the whole city planning and urban development fields, especially after the world wars, and the need of preserving European historical sites from destruction, had influenced those architecture and planning subjects, and spread the importance of historical preservation throughout the world. A little later, in the 1970s and 1980s, the historical preservation idea became of some importance in the urban planning and architecture academic community in the US. But, by then, it was already a little late to save American historical cities that had been bulldozed to open way for the United States to become the largest economic superpower in human history.

So, the lack of economic development and the backward character of their societies "helped" somehow Brazil and Colombia to preserve colonial towns, basically as there was no need to raze historical buildings to open the way for "progress" as it happened in the United States during the 19th century.

Here is an interesting article about the very recent history of the Historic Preservation concept in the United States, which explains why Historic preservation as part of urban planning was (and, unfortunately, still is) frowned upon by city officers in the US.