Would you accept a wizard that only casts spells 1 round in 10? Why or why not? That's every bit as much of a wizard as your Battlemaster is a warlord. Should be perfectly acceptable.
Sounds like every wizard in 1-3e.
And now, in 5e, it's still *technically* true since cantrips are cantrips and not spells. Semantics.
So, really, you just need a fighter with extra at-will powers, right? A "Tactical Combat Options Rules Module" that lets warriors trade ability score to damage or just the weapon dice but have an additional effect would be interesting. But likely unneeded with the options already available.
But attack cantrips really just let spellcasters *almost* keep up with martials. Cantrips are basically sword swing with a little kicker to offset the crap damage. (They need to take a class feature just to keep up and add their casting stat to damage). And any martial class can trip or push, having better odds at success due to not having a Str dump stat. So a martial out of the gate might have as many attack options each round.
More if disarm and cleave are allowed. At which point each martial likely has more options than a spellcaster will have offensive cantrips.
So, really, we just need an at-will utility powers.
But making those gets tricky, especially in a rules lite system. Because you're codifying what you can or cannot physically do. In theory, any physical task should be possible with a decent ability check. If the fighter gains an ability that lets them stand up quickly with an Acrobatics check, that means a DM cannot make a ruling to let a player do that. It's taking away a potential option from everyone else. It's not really granting more options, it's reducing them.