Tableau does not have this functionality.
There are ways that you might be able to script this using tabcmd and then you could merge the Excel sheets.
Whereas it isn't possible to export all of the crosstabs in a single click, there are multiple ways you may be able to achieve this.
First, through the UI of Tableau Online, when after selecting a view to render, you can select to view and then subsequently export the crosstab by clicking the "Download" button and then selecting "Crosstab."
Second, as Jennifer mentioned, you may be able to accomplish this via tabcmd. You'll want to see this documentation:
Third, in Tableau Desktop, you can export a crosstab by doing the following:
Select Worksheet > Export > Crosstab to Excel.
Finally, I also found the following article, which may be of use to you:
Hope this helps!