I don't think its necessarily because he himself wants the attention, but moreso because he feels that his father Destro and his way of beliefs should be the face of "Liberation" and not Shigaraki and the League. The latter are very out and open with their villainy, while Re-Destro wants the movement to have a more radicalist approach, as shown through the methods of Destro originally, plus his teachings being sold and spread to others through books. So it seems less petty, and more cautious because he fears the League's presence and actions may get in the way of their true plans.
That's what I think is interesting regarding how this arc has been set up, because Shigaraki has been developed alot recently, so it seems like its preparing for an opportunity that will allow him a big win, however we also just got introduced to the Liberation Army, and based on how they've been set up too, it seems very unlikely they will so easily be disposed of by the end of this arc.
I know some complaints regarding the Overhaul arc is that people wished him and the Eight Precepts remained a presence after that arc and weren't completely exposed of, so I wonder if the Liberation Army will take that spot as another new recurring group on top of the League.