I agree 100%. Often when I use increasingly powerful local models (qwen3.5:32b I love you) I mix in web search using search APIs from Brave, Perplexity, and DuckDuckGo summaries. Of course this requires that I use local models via small Python or Lisp scripts I write. I pay for the Lumo+ private chat service and it has excellent integrated search, like Gemini or ChatGPT.
EDIT: I have also experimented with creating a local search index for the common tech web sites I get information from - this is a pain in the ass to maintain, but offers very low latency to add search context for local model use. This is most useful with very small and fast local models so the whole experience is low latency.