The difficulty in optimising a 3.5 Fighter was more to do with the bad position they started out in and the need to have access to many splatbooks to crib feats from. In terms of play, deciding upon your exact value of Power Attack was one of the most complex operations to perform.
3.5 opened up more tactical options than power attacks, but, yes a large part of the complexity of the fighter was in planning the build. In 3.5, it was better to start a new player who wanted a 'simple' character with a Barbarian, for instance.
It also seemed that the martial powers in 4e tended to be more straightforward than many of the magical powers.
Complexity was more tightly correlated with Role than with Source. All classes got about the same number of powers, so faced comparable numbers of choices, even if they were very different choices that worked differently with their class features. But, the Striker role was inherently simpler, Leader & Controller more complex. And, Controller role-support was mostly in their powers (while classes of other roles tended to have their role-support in the form of class features), making controller powers more complex/powerful. The quintessential arcane spellcaster, the Wizard, was controller, the poster boy for martial has always been the Fighter, and was 'merely' a Defender in 4e. Compare fighter powers to wizard powers, and, yes, the latter will be more complex.
It allows you to play a completely nonmagical martial character capable of holding their own in combat.
So does the Champion. Like the Champion, the Battlemaster isn't just capable of holding it's own, it's a high-DPR character, the equivalent of a Striker in 4e. The Warlord was not a striker.
Its abilities allow granting allies bonuses to attack a target, allowing allies to take additional out-of-turn moves or attacks, moving opponents around, and bolstering an allies' health through inspirational speech. That is a lot of the Warlord's "schtick" there.
You're talking about 4 maneuvers vs 334. So, no, it's a varied selection, but it's not a lot of the Warlord's schtick. If the wizard only ever got 4 spells: Sleep, Burning Hands, Shield, and Unseen Servant, it'd be a fair cross section of things the wizard could traditionally, do - offensive, control, utility and defensive spells - but it wouldn't be "a lot," just a sampling.
If the DM wants to see player choices mattering, then I would argue they should do absolutely everything in their power to avoid interfering with the causal chain between player choice and consequences, between player information-gathering and the actual information of the world, and between the lessons they have rightfully learned and the structure of the resolution system.
There is no 'actual' causal chain or world, the DM is providing all that, already. Providing it in a way that lets you riff off the player and come closer to meeting their expectations
My point is that it doesn't need to be--and that it has sounded like people are arguing that the DM should be free to meddle in the consequences of every choice the players make, but simply choose not to do so, except when they do.
I'd say it's a matter of making rulings in favor of fun. That could very well mean that the players' choices really matter - a player who chooses to betray an NPC ally will get different results than one who chooses to support that ally, for instance - it could mean other choices - left or right, spiked chain or bohemian ear-spoon, etc - don't matter so much.
Emphasis mine. I am interested in the term "house rule."
It's taken me years to get used to using it instead of 'variants.'
I typically see it used as a term for DM's rule that players must accept or leave.
I guess I'd define it like I would variant: a formal, probably written, rule change that the DM uses in his campaign, typically from the beginning, or, if introduced later, with the players at least informed (if not also consenting or majority-consenting or something).