Let me do it this way.

We have a League Selection Screen.

What is the point of going to THAT Screen, to then go into a League... to check the Engine?
When you could have the Engine for Every League on the League Selection Screen?

So with MY option, you go to League Selection and viola, you can see at a single glance what Engine every League you are in is in. Then you can go to Available Leagues, and in a single glance know what every Available League has for Engines.

In the current method, you have to go to the League Selection screen (see how this is a common theme), but then go League by League to check. For some one like, say, RayMattison, with 752 Teams... this could be exhausting. Poor guy might die of dehydration before he manually clicks every team he owns to find the Engine for those Leagues.