@carlix and @pemartins

First off, please read this comment carefully and assume good will.  It might sound quite negative to you at first, but I'm really trying to see what can be changed, and therefore try different view points on this topic.

I can only check the comments in the Software-Center in Debian. There I see an upvoted, 5-star comment with some explanations why "Launch" in the Software Center cannot work, and later lots of 1-star "doesn't work" comments. That makes me wonder if adding Wine to the "Software Center" was the right decision.  With multiarch (i386 needed on amd64 systems) and workarounds as described in appdb.winehq.org needed for specific programs, I still wonder if going the graphical way really helps people (being able to right-click on an application to "Start with Wine", but not seeing any error messages, might cause more trouble then help. And expecting that you can "Launch" Wine is completely off). So my personal feeling is to not lower the entry barrier too much, in order to not make people having false expectations. In that way I think about removing Wine from the Software-Center again.

Now, ignore that for now, and let's consider other options:

You gave me one example of comments about the right-click thing, so you want the wine.desktop file installed.  Regarding the security-implications, and fileroller being preferred anyway:  I don't think this assumption is true on every system (based on what I remember from the last time I had a thorough look at this).  So this would need some investigation first.  Maybe there's a way to ensure Wine is not the preferred application automatically.

However, I'm thinking about a new package "wine-desktop-integration", which installs wine.desktop and maybe other things (e.g. winecfg.desktop, which so far nobody here did care to submit upstream :( ).  Would such a "wine-desktop-integration" package help? Or do you want this stuff in the "wine" package itself?  For the former I could just put a warning in the package, for the latter the security issue needs to be solved for sure, but even then I expect some opposition e.g. for "cluttering menus".

@pemartins:  Please elaborate.  What system/desktop environment (DE) are you on? Does your DE allow you to put files on the Desktop at all?  Do you have an applications menu?
E.g here (Debian Buster with Gnome as DE) I have the setting "Tweaks -> Extensions -> Applications Menu" enabled, and see the installed Windows application as expected in the "Applications - Wine" menu.  I can also start installed programs after hitting the "Super/Windows" key.  However I just noticed that Gnome 3.28 completely removed the option to show files on the Desktop.  You need e.g. the nemo-desktop file manager to keep this feature.  So I suggest you verify the contents of these folders (note that they might use translated names on your system, or be configured completely different):

$HOME/Desktop
$HOME/.local/share/applications/wine/Programs
$HOME/.local/share/desktop-directories

If you find the files there, or after a search somewhere similar in your home folder then Wine already works as expected, and the issue is somewhere else.

Is there anything else in the Ubuntu comments, that is actionable?

Are there any packages/distributions which do, what your request here (except the "old" Ubuntu packages which were superseded by "our" packages)?  E.g. as @pemartins confirmed, the wine-staging packages by upstream (winehq.org) don't do this (and I guess that is for the reason I stated in the beginning).  So I'm interested in seeing if and what others did.