This would be way better, mainly because Zsh is way easier to use for the average user. It has much better autocomplete, among other features 
I don’t see any reason why not. We could even install Oh My Zsh and make a custom theme for it, to make even the Terminal fit in with the OS 
. If not the default, maybe an option in Budgie Welcome would be nice.
To be honest, the average user would not have a clue what a shell was never mind understanding the differences between bash and zsh.
What we are talking here are advanced users who would be more than capable to switch shells.
I dont see any compelling reasons switching. I would much prefer to inherit the same shell as ubuntu - all development and testing would have been done using bash … so jumping to zsh will involve risks which I dont believe will be beneficial overall.
As to including a switch in welcome … A development section is something I would love to include e.g. installing vscode git etc. Just need someone to step up and develop this.