Chess Engine Paradox

There seems to be a paradox with regard to chess engine evaluations. Basically, 1) the deeper the depth of search, the better (more accurate) the engine evaluation, and 2) engine evaluations do not converge with depth -- going one ply deeper in search can completely overturn the previous evaluation. What does this mean?! Are evaluations completely meaningless ultimately, are evaluation only to be considered relative and not absolute at any fixed position, or are evaluations always a function of both depth and position? I suspect the latter, and thus that both of the others are also essentially true. Of what use are relative-only evaluations in comparing positions whose only common ancestor is horizon-effect distant?