You are very correct, the fundamental problem here is not that people don't read the EULA, it is that the world "agree" is not meaningful in this context, there is no equitable power relationship between you and the company you are "agreeing" with, they can insert any demand they wish and you have no ability to negotiate or power in the discussion. You should not have to read the EULAs, because companies should not be allowed to require that you waive your fundamental rights like this as a precondition of using their service. If you have a right to sue but every company can demand you waive it before you interact with them, you actually have no right at all.

If mandatory arbitration is allowed, the right to sue does not exist. You cannot have one but not the other.