Like another commenter, I consider it a blessing to be locked out of anything so thoughtlessly designed as to disallow access to anyone without a phone.
I have a similar policy for modal dialogs on websites: If I'm trying to read something and a modal dialog appears, I consider it a blessing, because it has just saved me time reading low-quality content, something I have found to correlate strongly with low-accessibility websites.
If I'm browsing without JavaScript and I'm not able to access the content, same story.
I've generally found it to be extremely beneficial for myself to easily back out of anything I find difficult to access, because low accessibility usually means low quality as well, and it allows me to use my time better.