Unlike App Clips, this would work with all iOS apps unless the developer opts out.
Moreover, it would be more convenient for the user. The app would be part of the web page just like an embedded YouTube video.
With Active X you could package a Windows program as a "COM object" that could be embedded in a rectangle in a web browser. This was part of a wider technology where you could, say, use a visual builder to embed a COM object as a visual widget in a Visual Basic problem.
It was a pretty good technology but had the major problems that (1) it was dependent on Windows and would make web pages incompatible with MacOS, Linux, etc. and (2) it had no sandboxing of any kind which made it unacceptable from a security viewpoint, even in a time which was innocent compared to today.
One problem: mobile apps expect to have access to the whole screen and not run in some arbitrary rectangle embedded in a web page
Two routes to embedding:
(a) do basically the same thing you do when you install an app except display the app in a web page. this will take as long as installing the app but the app will be able to do anything the app does except persist data because the app gets uninstalled when you leave the web page (unless instead of installing it later you can flip a switch to 'keep' it)
(b) boot up the app in a VM or container on a server and make it accessible by 'remote desktop' or video. This could be quick to start but would take resources on Apple or the developer's part. For many apps the system would be responsive enough that the demo is fair but for others (say something 'AR oriented' that uses spatial sensing) the introduced latency would be a problem.
Pieceable circa 2011 was acquired by Facebook: http://web.archive.org/web/20111006043944/http://www.pieceab...
Kickfolio circa 2012 (later app.io) raised $1M but shut down some time in late 2016 or 2017: http://web.archive.org/web/20120903014851/http://kickfolio.c...
AFAIK, both streamed the iOS Simulator to your browser.
Making a whole app available probably raises a lot of security and privacy issues; for a demo, you probably want something closer to a playable quote: https://tenmile.quote.games/