REAPER and Badge of the Brotherhood

I don't want to start off with a TLDR; So, I was wondering if anybody would like to talk about the active skill gem "Reaper" and the unique "Badge of the Brotherhood" but more particularly the line which reads ~(7–10)% increased Cooldown Recovery Rate of Travel Skills per Frenzy Charge~

Should Badge of the Brotherhood's Cooldown Recovery Rate count for the Reaper's dash ability, or do you think that would break the skill in terms of being too powerful to consider.

It shouldn't.
If it did it would be inconsistent for a thing to work on minion without it specifying minion.

Unless an item mod or passive skill specifically says it works with minions, it won't. Summon Reaper's dash skill won't be affected by Badge of the Brotherhood.

There are crucible nodes that have increased cooldown recovery rate of minions (and reduced minion duration).

one-handed weapons, T1:15% T2:25% (-10%)
two-handed weapons, T1:30% T2:50% (-20%)

Divergent Summon Reaper with Ashes of the Stars, 40~50%