This isn't the first time you have posted this story and each time you get told why the big bash draws big attendances but I'll tell you again.
The competition is played in the summer school break meaning kids are obviously off school as well as a good portion of parents off work and a good portion of society in general over the slow January period. Even for people who are working, it is normally no issue leaving work early in January. This means that the games can be played at any time.
Sydney and Melbourne have 2 teams and the other capital cities have one team. Each club only has to sell 4 home games (5 or 6 if they host finals which sell themselves). Given those numbers, if the average cricket fan goes to one BBL game in their home city each season you will still get sell outs at most grounds for each game.
That is one of the reasons it is drawing great crowds. But you are stretching to say it is THE reason.
I think if it was THE reason then they could shift Sheffield Shield or 50 over cricket to an evening slot and get the same great crowd at that time.
There are obviously additional reasons such as (1) they made the game itself exciting as hell for the kids and (2) they made it interactive as hell by improving the GAME DAY EXPERIENCE. They do that DAY-OH thing and the kids love it and that Greek thing. The players and staff are in a dug out on the sideline. I would need to go to a game to see what else is up.
I can guarantee you this: if the running of Big Bash was left to the same guys who run NRL clubs it would be like Sheffield Shield within 5 years.
Edit: I just googled Big Bash Game Day experience. They promote it on their home page with words like: "3 hours of excitement, fireworks, music and other entertainment"....I can't recall even reading the word cricket. The one photo is of a dude flying around with a jetpack.