Currently, HomeAssistant relies on the Matrix Client SDK for Python library for Matrix, which was last updated in July 2018 and according project page, the library is only “lightly supported” and they strongly recommend using the matrix-nio library. In addition to being better supported, the matrix-nio library supports E2E encryption which would be a nice addition.
The component already use matrix-nio, so enabling E2E should be trivial
There was an attempt to enable e2ee support in Enable matrix end to end encryption by alexyao2015 · Pull Request #112538 · home-assistant/core · GitHub, and it was closed because matrix-nio needed some changes upstream. Those have since been merged so in theory that HA MR could be re-opened and merged(?).
The stale bot that HA uses in github prevents me from replying to that closed MR and notifying the author (Alex Yao)