I suppose that colonies which were relatively sparsely populated and technologically backward provided opportunities to install a population from the mother country - USA, Canada, Australia, New Zealand; to some extent Argentina, Brazil. This basically created a copy of the original society (although much changed by now).
IIRC, the problem with finding a lot of gold was that Spain warped its economy. When the gold stopped, it fell into the economic doldrums. Local farmers or craftsmen often ended up competing with the best of their poorer counterparts across Europe. I read somewhere that the rest of Europe developed the economic infrastructure and activity to earn that gold from Spain, so in the long run benefited more.
The model for most empires was that the colonies provided raw materials for the mother countries’ economies; so industries that did the processing locally were to some extent actively discouraged, stifling industrial development.
Perhaps the best gift the empire could bestow was stability and good government that benefit the country after independence. Compare the British (or some French) ability to “know when to let go” against the sort of liberation wars that Portugal fought against Angola and Mozambique, to the relatively peaceful Commonwealth co-existence. This isn’t a fast rule though, one can point to India, USA, French Indochina and Algeria as examples where the mother country had to learn the lesson early and often.
Massive, massive case of Americanitis here. There were two great waves of colonialism, the first in the 16th century and the second in the 19th century. In the Americas, in the first wave of immigration you had massive immigration from the mother country which completely displaced or supplanted/suppressed the locals. So when decolonisation time came, the country was handed over to descendants of the settlers, or slaves as in the case of the Carribian.
In the second wave, in the 19th century conquests were for resources, strategic reasons or for pride, (Australia being the the odd one out here as being part of the second wave, but still resembling the first). This is what we talk about here.
There was certainly a difference between British colonization of North America and Australia/New Zealand (though those weren’t really as far apart as 16th v 19th centuries: there were no permanent British settlements in the now-US till the 17th century, and Australian settlements started when the US was still part of Britain in the 18th century) and later British colonies. And for that matter Spanish colonization was different still (ending with a demographic of largely mixed European-native population) than English colonies in either North America or Asia/Africa.
But the economic and strategic incentives in all the cases overlapped to a significant degree. But also the success in achieving the sought after goals varied widely. IMO it’s ridiculous to say Spain didn’t benefit immensely from gold in the New World, on some basis of it leading to later Spanish decline. So it can always be with easy money of any kind. But do you want tons of gold nearly for free or not? Of course you do.
Most other colonial equations were more complicated than that. To a great degree the viability depended on norms of international behavior. If everyone recognized that free trade (perhaps along with aid and international organizations, IOW kind of what we have now for relations among poor and rich countries) was better than having to run other countries, that’s one situation. But if, as was mentioned earlier, rival colonizing countries would freeze you out of trade with their colonies, even on economically misguided assumptions, that was something else. It’s harder to judge the benefit of colonies in the absence of that context, except in the extremes of colonies with large amounts of valuable commodities that could just be taken from the native people; or OTOH places that required a lot of intervention and development, which the colonizing society (by then) felt the moral obligation to provide, while the colony had nothing much to offer in return but a ‘market’ the colonizer could access almost as easily without being colonial master. The latter situation, along with changes in moral views about colonization, is what faced Britain and France by ca. 1950’s, for most of their remaining colonies.
If you want a really good example of a disastrous colonization attempt, Scotland’s Darien scheme went so poorly that Scotland needed to join with England Darien scheme - Wikipedia