Building on Alyssa's post --
At least some of the financial benefit of ordination of men is the ability for the school to offer a portion of salary as parsonage.
Before the latest series of Maharat/Rabba/Rabbi controversies it's my understanding that this was actually something that the Agudah recomended to their principals (2009 or so?) under certain circumstances as a way to save the school money in FICA and Medicare taxes.
That said, many schools don't pay parsonage because the lack of formal title or formal ordination for many of these women makes their status for parsonage more murky, thus not only hurting their own pocketbooks, but also the school's as well.
Many more details vis a vis orthodox women and parsonage available here: [
www.jlaw.com]