Issue 788571  has been merged into this issue.

That feature only flips the user agent between desktop and mobile, (as well as changing chrome's layout behavior more like desktop). If the site keeps other state about whether to serve the mobile or desktop version, like say in the cookies, then that would indeed not work properly, and there isn't really anything chrome can do.

If clearing site data "fixes" this, then that means you'll need to report this to the site owner.

Can be this investigated BEFORE bug is closed ?

I did investigate. But what do you expect to happen?

I mean this feature isn't really part of any web standard, and it's really like a best effort thing initially built around the time when mobile web was new, and most sites had less useful mobile versions. Things should generally be better now, but we can't force any particular site to improve

It would be great to know what is concrete reason of this concrete behavior + if this is possible to do something with this.

It can be potentially everything starting from wrong cache management to sending wrong headers, 

maybe it's required for example to add somewhere additional check if we get correct version ? (I mean - if we have in cache desktop version and we expect mobile, maybe in some specific situations we should ask website for file again?)

It's for checking, saying "it can be everything" seems to be not adequate and enough.

PS. Chrome is known as software going over or even creating some standards, let's continue it instead of saying "cannot be done"

Caching is not the problem. You can check the network tab in devtools. The entire page refreshes, and chrome requests the main resource again with different UA and max-age=0. In terms of this unspec-ed feature, that's all working correctly.

If you want to discuss how this feature should work differently, then that's a different discussion that I probably can't contribute much. +tedchoc maybe.

boliu@ is correct and offered the steps to investigate.

This repos the same on desktop if you open developer settings, initially load the page on desktop, switch to a mobile emulation mode, do shift-refresh.  You'll see it maintains the desktop layout.  This is definitely a site issue and no change to the feature will address that.  The site is not using responsive design principles to adjust the page to be usable on smaller desktop screens either so this is something you need to discuss with them.