I think Supercell needs to find a way to make Beatdown decks have a higher level cap. What I mean by this is that while Cycle decks are harder to master than Beatdown decks, Cycle decks at their best will usually beat Beatdown decks at their best (as OP mentioned).
Beatdown rules down in lower arenas, since Cycle players are not as good as their pro counterparts at 7k+. Cycle players at lower arenas are not experienced enough to use Cycle decks sufficiently to handle Beatdown.
However at higher trophies, the situation is reversed. Everyone is extremely good, so skill level is not the issue. It becomes obvious that Cycle decks dominate; Since everyone at 7k+ is a very good player, the discrepancy in win rate should not be the player's skill themselves. The only other explanation is that Cycle decks are truly superior to Beatdown decks.
One example of this is icebow. Tanks cards; i.e. beat down decks are supposed to counter siege decks. Howev...