I agree that "edges" is a weaker implication of flat-earth than the others - but I don't think it's unjustified. For one thing, the atmosphere is not purely transparent, so it should be impossible to see the sun through it if it were infinite in (horizontal) extent; for another, the sun has to come up somewhere.

These challenges could be evaded by videogame physics, for example, but such would be in conflict with human intuition.