Look at what happened when Firefox switched default search. The default search on Firefox is now worth far less than it was before as they lost huge amounts of browser market share.
Bing is down to 2.5% market share , global and all platforms.
That's $correlation !== $causation. You can't for sure isolate "default search engine" as the only variable (because it wasn't), but I'm sure it was a significant driver.
Remember that Google was pushing performance, had a massive install base and marketing budget during those years.
There is a huge amount of friction added to a system (in this case, the browser-web ecosystem) when a major change like the default search engine is changed. The aggregation of all frictions is what causes users to alter their behavior or seek other solutions to reduce that friction. If iOS were to switch, some users would figure out how to change their default setting, others would simply see an increase in frustration with "the product" (meaning iOS + web search). It is likely to cause some migration, but probably not a significant amount until and unless other frictions are added.
Remember that Google was pushing performance, had a massive install base and marketing budget during those years.
There is a huge amount of friction added to a system (in this case, the browser-web ecosystem) when a major change like the default search engine is changed. The aggregation of all frictions is what causes users to alter their behavior or seek other solutions to reduce that friction. If iOS were to switch, some users would figure out how to change their default setting, others would simply see an increase in frustration with "the product" (meaning iOS + web search). It is likely to cause some migration, but probably not a significant amount until and unless other frictions are added.