OK, the intent was indeed actually to only show the icon (like elsewhere). So that makes the current issue no more a bug, but an improvement request.
For me, it's two fold (from a "product" management perspective): either we just close this bug as wontfix because we want to keep the complexity low, or we add a new column variant named for example 'last build trigger - long version' and reintroduce a column with the old behaviour.

If we were on a big product, I'd say the first solution may be better. In our case, I suppose the second case is feasible since the codebase is still pretty small. Though we sure want to reuse as much code as possible if we introduce that second column being a 'long' variant of the current one.

Columns can have configuration. Why not add a checkbox or dropdown menu to configure column behavior (rather than add two different, but similar columns)?

Advantages would be that it requires less space in the column selection list in the view configuration, and you can more easily switch from one form to the other.

Additional note: for that new column, to not have the issue that led to JENKINS-22557 we certainly want to limit the max number of characters shown to some hard value, and for example show the full version in a title (if there's more).

Thanks a lot Daniel, I wasn't aware it was possible. So that's obviously what I'm gonna do.
Thanks again.

Awesome. So, we can look forward to a global and local configuration for the column behavior?

Absolutely. But currently having a hard time to do find the time to do it. So if nobody submits the corresponding pull request (hint! Hint! ), it's likely to take still a few weeks before this can be done.
Cheers

Code changed in jenkins
User: Lukasz Jader
Path:
src/main/java/org/jenkinsci/plugins/buildtriggerbadge/LastBuildTriggerColumn.java
src/main/resources/org/jenkinsci/plugins/buildtriggerbadge/LastBuildTriggerColumn/column.jelly
src/main/resources/org/jenkinsci/plugins/buildtriggerbadge/LastBuildTriggerColumn/config.jelly
http://jenkins-ci.org/commit/buildtriggerbadge-plugin/94eda6518004133f0f11af0c38ee14d1ad593669
Log:
JENKINS-26186 Enable changing display format for Last Build Trigger
Column

Users can now pick how to display build Cause in mentioned column,
since not all users want to see long descriptions.

By default column will display only icon for build cause.

I've prepared a Pull Request for this issue:
https://github.com/jenkinsci/buildtriggerbadge-plugin/pull/15

Code changed in jenkins
User: Baptiste Mathus
Path:
src/main/java/org/jenkinsci/plugins/buildtriggerbadge/LastBuildTriggerColumn.java
src/main/resources/org/jenkinsci/plugins/buildtriggerbadge/LastBuildTriggerColumn/column.jelly
src/main/resources/org/jenkinsci/plugins/buildtriggerbadge/LastBuildTriggerColumn/config.jelly
http://jenkins-ci.org/commit/buildtriggerbadge-plugin/0d0fdb4b22b1bccafb262d82ef88a35fe6537200
Log:
Merge pull request #15 from jenkinsci/trigger-column-configurable-display

JENKINS-26186 Enable changing display format for Last Build Trigger Column

Compare: https://github.com/jenkinsci/buildtriggerbadge-plugin/compare/40ac15121da4...0d0fdb4b22b1

Fixed wit PR; released with 2.1 version.
If somone encounters any other issues with this column please report it as a new issue.