hi Valentin,
UI5 is just javascript so there's no mystery, there's nothing really "SAP like solution" - this isn't ABAP and SAP does not set the trend, they just follow the trend.. so if their framework doesn't have A or B you just go and code yourself. (at least that's what I usually do)
About your question, I'd suggest you either extend or "re-write" (from scratch) the SAP Control into your own because I hardly think you will find any "easy answer" - looking at branch 1.26 you would need to re-implement the Renderer (IconTabBarRenderer) and make sure it writes the DOM for all tabs instead of just the "selected" one and the "_rerenderContent" on the IconTabBar to just adjust visibility state of the nodes. Also, looking at the same code there are several things you can make it better, so the option is really yours.
Hope it helps,
Dan.