You can to the same extent that you can access a smart phone on the go. You just have to remember to bring it with you. Given how often I "forget" my smart phone at home, the "access anywhere" isn't a huge selling feature for most things to me. While I do use web-based email, I tend to prefer things like paper tickets for events and paper receipts because I actually find them to be more convenient than digital. This is because having to have a smart phone with me at all times that could get lost, stolen, damaged, malfunction etc. and is a single point of failure in the event thereof is the polar opposite of my definition of convenience.
No one has made the argument that paper is without problems. Only that it has way fewer problems than digital. That, and that the businesses and shills that are trying to force digital-everything are evil monsters that belong in the same rung of hell typically reserved for murderers and people who talk at movie theatres.
I suspect that many people associate durability with electronic media simply because it becomes obsolete so rapidly that we don't experience it in the same way. We don't know whether that dusty floppy disk or CD-R is readable since we disposed of our last computer with a drive, or we associate the failure of a flash drive with a cheap drive rather than the intrinsic properties of the media, or we attribute it to abuse. We rarely have the opportunity to use something until it is worn out, or pick it up after a quarter century in storage.
Modern media is incredibly fragile. The chief advantage it has (in terms of longevity) is its digital nature, in our ability to reproduce it exactly. Yet that is only an advantage if we actively maintain our archives.
The same thing has happened with flash drives already, how do you identify a good flash drive? If you aren't careful you'll end up with a counterfeit but even the genuine articles have shaky reputations and manufacturers change the internal parts all the time.
That said, such things did happen in the past. Paper is the classic example since the manufacturing process affected its longevity, yet many other materials are graded based upon their properties.
Or probably because paper or other media has already stood the trial of time, there are some papyrus dating around 2500BC that’s more than 4000 years ago, now think if any of the tools needed for current media will be available 4000 years from now.