You're dreaming of what wolfram alpha is trying to build.
Edit: funnily enough, they parsed the input slightly wrong but you can quickly get to your answer.
Google Assistant (aloud): $3,004
Seems pretty straightforward, no need for a web page.
Actual current results: "Sorry, I don't know how to help with that yet"
While in the interest of "privacy" Google limits the amount of data the banks and others you interact with get from any competing solution, they will sell all of it in Ads Data Hub which is a Google Cloud product. So not so much in the interest of privacy but much more in the interest of Google selling more cloud products.
User: I can afford a livable four walls and a roof from a small amount of savings, without needing to mortgage decades of my future. Brilliant.
The problem with that is that if a poor person can afford a house with cash, then a slightly richer person would just go, "wow, I can buy a really big house! Or two!", and suddenly there is no more space.
Maybe they wouldn't be allowed to buy two, because in "a perfect world", a place to live is a necessity, not a profit vector. Keeping housing supply limited to boost house prices, to appeal to house-owning voters and wealthy landlords, to extract six figures of money from normal people over decades, is nothing like "perfect".
Here I say "landlord epxloitation, profiteering from necessities, houses left unlived in as investment vehicles for the international super rich, NIMBYism and entrenched residents voting against housing stock, AirBNB, broken zoning incentives" and then you say "FREE MARKET it's rich people's right to buy up everything and if you disagree you're dumb, free market is best market". And then we disagree to agree and both leave unhappy. Is that an approximately good summary?
We don't need to determine who gets which for this comment chain, we only need to question whether a 30 year mortgage should be the default way for a normal person to keep the rain off their bed, someone who isn't thinking of a beach condo in Malibu or a NYC penthouse, whether that is the best possible "perfect" world. I think it isn't.
User: Hey Gateway, what's the monthly payment on a 20-year mortgage with 3.9 APR?
Gateway: Here's your calculator, already prefilled with the data taken from your query.
Done.
The problem with all these little sites is, besides bloat, that the "Oh, neat, they can hook me up with lenders. Let me take a look." ends up with user getting malware and/or scammed. The problem with Google is that they can hardly be trusted at this point to do things like this in the interest of users. They want to be the frontend through which you access the Internet.
I used the word "Gateway" in my example as a placeholder; my imaginary perfect world recognizes that things like "currency conversion", "song lyrics" or "mortgage calculator" are data[0], which should be separate from the frontend used to access it. I dream of the Internet where things like these are API-driven and do not involve loading anything other than what's requested - neither ads, nor "value-adds", and definitely not all the rest of the webpage surrounding a mortgage calculator, which is bloat obstructing requested functionality.
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[0] - yes, even mortgage calculator; it's a mathematical model, an algorithm, and code is data.