I've been an aphid enthusiast and expert for 30+ years (
https://aphidtrek.org/). As somebody mentioned elsewhere, there are thousands of aphid species, each with different biology, behavior, and most importantly, host plant preferences. In my garden I generally don't worry about most species of aphids very much. With good crop and plant diversity, ground cover of plants or organic material, there should be plenty of biocontrol to help you out. Also, many aphids will go away on their own during the heat of summer. There are exceptions. I'll try to squish and otherwise eliminate cabbage aphid because its waxy coating (some predators are dissuaded by the wax) and habit of living deep in the inflorescences or curled leaves mean that it will persist throughout the summer. Once, on my apples, I had a roaring conspiracy between ants and an apple feeding specialist aphid called
Aphis pomi, the ants helping the aphids stay abundant all summer, which is rare in tree feeding aphids. I prevented the ants from accessing the aphids for one summer (using sticky traps wrapped around the trunks), and the cycle was broken. That said, many ants, when tending aphids, are not actually protecting them; they are simply gathering honeydew and harvesting aphids as needed as well.
Bottom line for me is that the key principal of Integrated Pest Management (IPM) is important here: know what species of insect you have (i.e., not just a broad category like "aphids" or "caterpillars"). Knowing this means you can predict your insect's biology and host range, and then you can act accordingly.