You are not properly evaluating the samurai archetype, in my opinion.
The battlemaster is stronger in tiers 1 and 2, but in tier 3 the samurai is roughly equal in terms of damage output because of the Tireless Spirit feature. The samurai pulls ahead in damage output in tier 4 because of Tireless Spirit and Rapid Strike.
There's a statistical analysis between the two archetypes, which I can't find at the moment. But it compares the damage output of both archetypes in each tier of play. Fighting Spirit and Tireless Spirit also both have amazing synergy with Elven Accuracy and Action Surge.
Battlemaster is the safer choice, since most games don't make it beyond tier 2. However, if you're playing in a campaign that will make it to tier 3 or 4 - samurai is a solid choice.