Right now the only way I see to do this is by adding the HTML code directly to the page
That’s how I would do it. Though if you do it this way it would be better to stick to using Text editor mode instead of the Visual.
but that seems so contrary to CSS.
What do you mean? Tables are created using HTML markup. CSS is only used for when you want to style your tables.
If you aren’t familiar with the table HTML markup you could use plugins that create tables for you. Ex:
https://wordpress.org/plugins/tablepress/
https://wordpress.org/plugins/easy-table/