slobster
Hero
The way I'm reading it, the fighter can make two attacks in the first two rounds of combat. After that, he's too tired to fight that way the rest of the day.
In 4e terms, the 5e adventuring day is one big encounter, and these abilities are your "nova" abilities that you would want to use as early and as often as possible.
Unless there is a reason to wait for the opportune moment to get the biggest bang for your buck, so to speak. In 5E that might be advantage. The fighter should wait for a time when he has advantage to use his extra action, otherwise it wouldn't be as powerful as it would be if he did. Not only that, but he should wait until he can really unload on an enemy(ies) that can take the extra beating. No reason to attack an enemy bugbear and get him down to 2 hp, then burn your extra action just to finish the job that anyone else in the party could have done as well, without using up daily resources.
I don't know if DDN has it right, yet, in encouraging the fighter to use his limited-use ability strategically, but it seems possible to me in theory.