The infantry had to form squares if faced with cavalry (even if the cavalry wasn't charging). That was very disadvantageous because this all-round defence formation was very slow-moving if not completely stationary. It was also very dangerous if there was a threat by infantry and cavalry at once because a battalion in square formation was only a fraction as strong against enemy infantry as in a line formation.
That was - even before we factor in any artillery - an interesting combined arms benefit for those who held up a cavalry charge threat while really attacking with infantry.
The modern conventional battlefield - hypothetical as it is - would most likely not see uninterrupted front lines as during the World Wars and the Korean War. The force density is simply not large enough; we would see brigades (actually clusters of battalions) with huge gaps between each other. These gaps would need to be filled (and if possible also controlled) by reconnaissance units and small detachments.
Reconnaissance units may well prove to be the least-prepared branch in the next major conventional war. The whole branch seems to be completely under-resourced and short of modern requirements in most if not all countries (and my previous comments on the subject cover just a tiny bit of the problem).
The aforementioned gaps mean that units don't need to "break through" in order to reach the enemy 'rear'. Small companies could (if the terrain isn't too restrictive) maneuver around a brigade and threaten (and hit) it from every direction.
Now imagine a combined arms company with dedicated doctrine, TO&E and training for independent armed recce. Many such companies (let's call them 'heavy skirmishers') could swarm out and fill the landscape like water would do. They flow around enemy strengths (rocks) and exert pressure on them from all sides, even eroding all parts of the rock that aren't strong enough.
The same flood of heavy skirmishers also drowns or breaks all small, weak opposing objects in their path.
The brigade could waste time by attempting to chase and destroy the more agile and really small heavy skirmisher units. One of the many inadequacies and problems of such a response would be that the brigade's combat units would be busy on the tactical offensive and likely run into many ambushes without scoring enough decisive blows against the many harassing units.
The more likely response is the delegation of combat units for all-round security (cover) missions. A brigade that provides all-round cover for its 'support' components would be very vulnerable to a well-directed blow (or even two).
It would be quite impaired in its ability to execute retrograde movements like delay or an withdrawal - it would effectively be a moving pocket at best. This includes cut-off support routes.
Said brigade would furthermore have inferior (so-called) "situational awareness" because the more combat-capable heavy skirmishers would easily dominate over the usual weak recce or even observation units.
Finally, this 'moving pocket' brigade in all-round defence formation would hardly be an offensive threat.
A promising counter-measure to the mentioned corps-level tactic (or operational art) is a competition for the more effective heavy skirmishers or the employment of dissimilar counter-forces (attack air power, for example).
Almost everything in warfare is susceptible to countermeasures, so this shouldn't surprise. A race for the stronger heavy skirmishers would resemble the quest for the stronger cavalry of earlier ages. You can easily look back to Alexander the Great or, more appropriately, to Hannibal's Cannae and Zama battles. The fast-moving cavalry that was able to hit from behind had been subject to a competition for millennia. The side with the better cavalry often had the decisive advantage.
Today's armies may resemble cavalry armies with their full motorization and partial mechanization.
That analogy is nevertheless rather poor. Unit speed isn't really proportional to vehicle speed. Units move much more slowly and react much more slowly than a single vehicle. Even a single battalion is a nightmarish convoy of vehicles. A company on 60 km/h tracks is therefore much more agile on the battlefield than a whole brigade on 100 km/h wheels.
The brigade as a whole is rather clumsy, while small units are agile. That turns small units into a better equivalent of cavalry.
In the end, we're lacking light cavalry (most people associate horses with "cavalry", so I prefer 'heavy skirmishers' as working title).
I assume that companies are the right compromise for the 'heavy skirmisher' concept. They can be numerous enough, have enough redundancy in functions, are agile enough (sufficient survivability) and are powerful enough to overcome both soft support units and enemy armoured recce units.
Now compare this understanding of armoured recce-alike companies with the weak armoured recce and armoured observation formations of modern armies.
Field manuals speak of widths where I think of areas if of any geographic limitations at all.
They focus on recce where I think of dominating the gaps.
Furthermore, orthodox armoured recce units up to battalion aren't combined arms units in German, French or U.S. armies.
OK, that was a glimpse of what I'm working on in regard to operational art in ground war. I could easily fill fifty to hundred pages with the modern ground operations topic, but it's still a work in progress (as everything in the art of war should be). The logistics part and mind issues (morale, daring, endurance) are especially tricky.
"Trading the Saber for Stealth" may be an interesting read for those interested in armoured recce today. It approaches the subject from a specific U.S. direction, but adds many useful points.
The French call "vacuum areas" what I call "gaps" (well, actually "espaces lacunaires"); see "Fighting in vacuum areas".