Your first disagreement is a misunderstnading. I separate the lareg area recce in armored cav squadrons and LRS. The LRS are meant for stealthy, slow work - especially observation.

The Cav would be agile, combat-worthy to some degree (against support/recce troops and against combat troops with the advantage of surprise/ambush) and fully capable of "maintain eyes on the target and battle handover to another unit. I think we also need to keep in mind the role of reconnaissance forces as an economy of force.".
I don't think that brigades need to be fully capable stand-alone forces, though. They should swim in an ocean of recce troops.

"As a company commander in Iraq, I would routinely use a squad or fire team as a recon force; I found eyes forward to be valuable even at my low level. Reconnaissance at all levels can be decisive - same for counter-recon."

Of course, but the timely recce effort of an infantry company in a major war has an effective radius that equals maybe ten minutes of driving (unless we talk about very, very open and featureless terrain).
I expect a degree of agility and I fear that enemies might have a degree of agility that necessitates an early warning more on the order of at least an hour for you'd otherwise be surprised when relatively unfit to fight.

again: "The real recce should be a Corps thing and should provide ~90% of the non-combat info on the enemy."