This may be a 'noob' question, but...
It doesn't seem possible to modify the WP-Login page via PHP (eg. add the get_header() code or new DIVs) to match the site theme. That is, without hacking the core, of course. (If there -is- a way to do this, please let me know!) And -yes- I am aware you can create a login template, but you can never get -rid- of WP-Login because it seems necessary for various core login/logout functions. (Again, if this has changed with WP4, please let me know!)
So, I've taken to simply adding the DIVs I want via jQuery(). Nothing extravagant... just a 'header' and 'footer' to match the site theme.
My question is: are there any reasons to -not- do this? ie. security concerns or other problems I haven't considered? I ask because there must be a good reason why this is the -one- place in WP where you can't use a 'template' page and that seems odd to me.