A lot of how a eikon interacts with the material world depends how what the people who summoned it wanted it to do. Given that Odin/Zantetsuken supposedly dates back to Allagan times, I could see people taking a look at what the Allagans were able to do to Bahamut and the Warring Triad and getting creative to minimize whatever they were summoning from getting sealed in Azyz La.

As far as we can tell, Zantetsuken tempers one person, and one person only; whoever it is that picks it up after the last tempered user of Zantetsuken was killed. Compared to the other eikons who temper almost without thinking about it (for the most part), that's very, very sophisticated. It also makes it really hard to actually stop the eikon as after killing it's bearer, the weapon has to be destroyed and that means someone has to handle it. Also, Odin takes a while to show up, which would give credence to people thinking he had been killed. If you wanted to trick someone into thinking they'd killed an eikon, it's not a bad set-up. For one thing, it'd never have to be summoned again which is what seems to be the biggest hurdle in eikon creation.

If the Summoner's relic quest is right and Zantetsuken/Odin was sealed up in Urth's Fount, why seal them there and not in Azyz La with the rest of the Warring Triad? Given that event happened late enough for people not to forget about it, I'm thinking that might mean Urth sealed Zantetsuken/Odin after Syrcus Tower fell. In which case, I doubt the Allagans ever figured out what was going on with Zantetsuken/Odin which is saying something.

If anything I'd say Zantetsuken reminds me more of the Knights of the Round or Shiva. It's essentially an eikon feeding off a person's aether only instead of being the armor, it's the weapon this time. Really makes me wonder what would happen if Zantetsuken was used by an Echo-user for a long period of time...