As far as I can tell, it already does this, and it's my most hated "feature". The delay while it does the search, combined with everything shuffling around at the end of that delay is terrible for me.
Personally, if I want to use the web, I'll open a browser. That's not the role I have for my OS, I don't want. And if it does have that capability, providing an alternate search engine should be doable, and it should respect my default browser.
It doesn't do this, because it's not smart and treat everything the same way. You first need to figure out what kind of content the user is talking about, and then go around that.
Microsoft system doesn't care if you're typing calc.exe or John Smith or 8x9 it will do the crappy web search, crappy app search, crappy store search, crappy calendar search, and vomit a mix of useless results in your face.
That's what makes it "hard" to do it right, and frankly something that microsoft just doesn't have in their dna (if they did, their start menu search wouldn't be so horrible). I think an OS that did it right would be improved, and I hope to hell and back that microsoft won't try it because they will never succeed at that.
There has simply never been a product or feature in the search world (online or offline) where Microsoft got it, everything they have that works is when they dropped their idea and just copied whatever the other guys were doing.
For me they just don't get search, like, the very idea of search or not just searching, it's understanding what you're searching for. And when you bring that down to the start menu, it become super clear and obvious that they're out of their league.
It does do this, if I put 8*9 in the start menu a little embedded calculator comes up that says 72. It does also prompt me to "see web results" for 8*9 though.
It doesn't, at least not in the way it should. It's not windows figuring it out and giving you a specific result, it's just a webview into Bing, and bing that show the results that way. That's why just under the calculator you have a link to a streetwear clothes brand.
You might think "so what, it does work" but 99% of the issues in the start search are due to this offloading to bing that is not aware of your local computer and data.
Personally, if I want to use the web, I'll open a browser. That's not the role I have for my OS, I don't want. And if it does have that capability, providing an alternate search engine should be doable, and it should respect my default browser.