Well the initial theory behind density bonusing is to provide on-site (or in the immediate area) amenities to offset the social "cost" of increased development. For example, parkland dedications are usually done through the subdivision process, but if you're densifying an established area there is no actual subdivision, so no new parkland, and the new residents add strain to the existing parks in the immediate area. Density bonusing would, in theory, account for this by creating investments to improve the parks in the immediate area. Local impact = local improvement.
With the affordable housing thing you're right, that link isn't all that strong. Yes, some affordable housing is being lost with new development, but that's independent of the density of the development (taller buildings don't cause more affordable housing to be lost). And it doesn't seem like the affordable housing is necessarily being provided in the area where it was lost.
In reality, I'd (as an outsider making wild guesses) say this is a hack to get around the fact that the Province is dropping the ball when it comes to affordable housing. Technically, housing is a provincial responsibility so HRM can hardly justify using general revenues to enter that realm. But of all the provincial ball dropping, housing has to be one of the worst, and there's a strong desire from HRM residents, politicians, and staff to pick up the slack. Density bonusing is the hack to get around that division of responsibilities problem; it's not HRM providing affordable housing, it's developers
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In a perfect world we'd just set taxes appropriately and use it to provide appropriate affordable housing, but this isn't a perfect world
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