Without the coolness it becomes an obvious balance mechanic with little story connection. It's only half an idea.
The playtest is designed to let us provide feedback as they "bake" the ideas. I agree with what seems to be a consensus that this idea has potential but needs more work (on the time, on the process, on the limits, etc.).
My suggestion would be to consider some basic rule for all or most items but to have many items require their own specific attunement processes. This could allow for the simplicity of a system for most items (which may be a simple, time-based system) but the mechanical niche for items to have their own process for race-based, class-based, sacrifice-based or quest-based attunement. In this way, this thread becomes a treasure trove of ideas.
For a racial item (Axe of the Dwarven Lords), attunement may only be possible for dwarves -- or there may be some level of attunement only possible by dwarves.
For a class item (Staff of the Magi), attunement may only be possible for one or a few classes (wizard, warlock, sorcerer).
For some items, a sacrifice may have the appropriate flavor. For a Stormbringer like item, sacrificing/locking a hit die is an interesting idea.
For some items, you may need to complete a series of specific questions (usually left to the DM to integrate into an ongoing campaign). The Rod of Seven Parts may require specific quests to unite the various segments.
The rules are flexible enough that I will likely do this myself regardless of the system rules.