Straight to the point:
File for tests:
On certain cases, like the example posted by @APEC it makes more sense to have a dedicated offset edge slide tool, rather than using the bevel tool for this, see: Right-Click Select — Blender Community
Just my 2 cents.
This issue is very annoying because of a lack of offset edge slide you need to use extrude and the bevel tool, though the bevel tool acts in an undesired way, so on top of the already tedious workaround for not having an offset edge slide you are also cleaning up broken topology.
The current workaround.
APEC, what did this model look like before you did the bevel?
My next big project as a volunteer Blender developer is going to be in the area of improving stuff like this. It is harder than it may seem, because of the issue of what to do when overlaps start to happen.
Unfortunately I have other stuff on my stack to attend to before I can get to this project.
it’s just a flat mesh example, similar to @Lamia example.
We started talking about it on another forum, but decided to post here to bring attention to this issue
Originally we wanted to select border edge and Bevel it, like this (because Offset Edge Slide didn’t work as expected)