Many Linux users download Arduino directly from the Arduino website rather use what comes with the Linux distribution, since the upstream-provided version is up-to-date while the version in the distributions (especially in stable/LTS versions) is outdated more often than not.

Providing an AppImage would have, among others, these advantages:

• Works for most Linux distributions (including Ubuntu, Fedora, openSUSE, CentOS, elementaryOS, Linux Mint, and others)
• One app = one file = super simple for users: just download one AppImage file, make it executable, and run
• No unpacking or installation necessary
• No root needed
• No system libraries changed
• Just one format for all major distributions
• Works out of the box, no installation of runtimes needed
• Optional(!) desktop integration with appimaged
• Binary delta updates, e.g., for continuous builds (only download the binary diff) using AppImageUpdate
• Can GPG2-sign your AppImages (inside the file)

Here is an overview of projects that are already distributing upstream-provided, official AppImages.

Do you think this would be useful?
I'd be happy to help producing an official Arduino AppImage.