Are you selecting the option to apply  the master page
and CSS to all sub-sites?

Yes, but it seems that when I create a new site, I have to go into the
site settings for the new site  and tell it to inherit from the parent
site. It seems that if I am telling the parent site to push the settings
to the children sites, I shouldn't have to do this.

That action only pushes the master page/css selections
on currently deployed sites. In order to do this when
a new site  is created, I would explore the possibility
of using either a custom site definition or web
application feature. Sorry, but I'm not a developer
so I can't go into detail on either of them.

Afraid that's just how it works. The default master page/CSS come from
the site  template chosen when you create the site, the option to apply
to all sites only effects sites already created.

I also find this 'feature' quite frustrating.
So much so, that I had one our developers create a simple application,
which can change the theme  on 1 or many sites below a starting URL.
I would be happy to share this with you, if you contact me directly by
email.