Without seeing exact examples, it's hard to properly refute your point, but differences in group strength would easily explain this. You wouldn't expect the same points tally from a group containing Montenegro as bottom seed versus one with San Marino as bottom seed. Consequently, fewer points could still indicate a better performance, and a better team. Similarily, coming third - and missing qualification - could easily come down to a freak result, like the group winner slipping up at home to second with the group already won. Does that make the third placed team any weaker?
As a chess player - which uses the same system to rank every player from beginner to World Champion - I can say the Elo system is statistically very fair. You may have to adjust it for football a bit - reduce the importance of friendlies is the obvious one, but that's easily done - but it doesn't have the flaws you suggest.
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