It would make the app more recognizable to Commons users.
Also, the current logo that I quickly designed is quite ugly.
WMF abandoned the Commons app in 2014: https://lists.wikimedia.org/pipermail/mobile-l/2014-September/007974.html
Misaochan and I have maintained it ever since.
A few years ago I used the Wikivoyage logo for the non-official Wikivoyage app and after a few months a WMF lawyer got Google to take down the app. So, it sounds obvious but before using the official logo, better make sure we have WMF's agreement.
At https://phabricator.wikimedia.org/T127678 Nemo_bis wrote:
If Nicolas will want to ask access to trademarks, distribution channels (e.g. on the markets) or other, that will be a separate request.
... so here it is :-)