We used to be able to go into places and be able to brandish our weapon. At least this was true for Burger Shot in IV. It was also true for Ammu-Nation in the older GTA's. Now you can't even hold any type of weapon or even punch anyone indoors. I wanted to murder the clerk at Ammu-Nation for old times sake (had fun doing this in III) and I couldn't even take out a gun.
This doesn't make me hate or dislike the game or think any less of it. I just feel it's a tad disappointing why you can't shoot people indoors. I think that's the reason people want interiors anyway.
And for the record, I checked out the arena and you can see that the interior is there but you just can't enter. It could be used for something at some point.