These concerns have been raised by clans, tribes, cities, and countries in receipt of migrants since the dawn of time.
You're correct that migration needs to be balanced against the ability of the services and existing resources to support migrants, while acknowledging that migrants bring with them needed skills and investment.
You're probably also correct regarding the stability of housing and cost of living. That's how things are in Australia at present in any case.
However, asylum is a special class of migration. You're not accepting migrants because you want them, but because they will face persecution if you don't. If a stream of Europeans arrived on Canada's shores by boat, and they faced imprisonment on undue punishment if you returned them, would you provide them shelter?
I don't really think that this is true at all.
In the past the USA might have been appealing because there was real opportunity. If you show up, and work hard, there's a good life in a stable environment for your kids and their kids. Those financial opportunities don't seem to exist anymore, and the political and social environment seems... undesirable for migrants.
Presently the USA might be desirable for people already in the Americas because you can get there, and the currency exchange is favorable.
I wouldn't want to make generalisations about Africa. There might be some locations on the continent that would be suitable, but IDK about that. You certainly wouldn't want to be wealthier than the local population, because that dynamic wouldn't continue very long.
I don't think there's a sensible answer to OP's question. I imagine that only a minority group from Europe could really require 'asylum' (like Jewish people during WWII), and the answer depends on the nature of whichever group is seeking asylum.