"They show the best of the best of Broadway, some of the blockbuster favorites...and this is a bad thing because why? Because they don't do Next to Normal and In the Heights? Acquiring the licensing and distribution rights for new shows like those would be so restrictive that it wouldn't be worth their effort.
How do you know that using older showtunes won't attract audiences? Maybe there isn't an immediate correlation with increased Broadway sales, but how will theatre benefit in the long run from a generation of kids thinking that show choir and musical theatre are cool?"
It's not a bad thing. I am not saying they should use songs from current shows because, as you said, there is not much new out with an original score. And you are right, the older show tunes may attract audiences to Broadway in general. However, if they are not singing songs from shows currently on Broadway they are not attracting audiences to particular Broadway shows.
For example if they were to perform songs from Next to Normal or In the Heights they would be making the audiences more familiar with modern Broadway shows which may bring more audiences to these shows specifically. You were right about the licensing though and it would not be worth their effort. I am trying to say that Glee is not helping attract audiences to specific shows currently on Broadway. Even if they were to perform songs from modern shows, there is no way of telling whether or not this would help bring audiences to Broadway, it is merely speculation.
"There’s nothing quite like the power and the passion of Broadway music. "