It’s not just accessibility. I’ve last track of the number of times I’ve seen a mobile website with a table that extends past the right side of the viewport and zoom disabled. You can’t scroll, and you can’t zoom, so you can’t read the table.
Maybe this is a good place to ask since there's a lot of web devs here: What is SO effing hard about drawing within the screen on web?! I can't tell you the number of times I've seen this issue. Just the other day I saw reddit's sign up form is totally broken on iOS, you have to swap between landscape/portrait multiple times and hope whatever garbage layout engine it uses redraws the button inside the screen.
As soon as you put real data into a website, especially if the website is a CMS that you've handed-off to a _non-technical_ client, it's going to overflow every pretty, grid-based box.