Scraping the data off of rendered web pages is possible, yes, but it will break anytime the other site changes the way they display the table. API's don't have this issue, because they're set up specifically for other people to access data without constantly breaking them.
It's not worth any of us spending time developing a solution without an API to access the table data. If it's a bad look that we have the men's table and not the women's, the solution in my opinion would be to remove the men's table.
The existence of the table on the home page is just a side effect of the old FeverBot, back when there was more regular discussion on the forums about the league table. FeverBot needed a way to display the table, which we could just pop on the homepage too. There's plenty of other places on the internet to view up-to-date and live table data so I don't think it's an issue removing it.