Cavalry should be strictly superior to infantry in all respects in ideal terrain. When a country has been able to build a mostly or fully cavalry force in the past they have always done so. The chief disadvantages to the maintenance of a cavalry force are as follows:
* the need to support large stud farms to replace losses of mounts. This is extremely expensive and absolutely mandatory if you don't want your mounted cavalry to become infantry after the first clash
* the caloric and other health needs of horses. A US Army horse during the American Civil War horse required ~3x the food by weight of a standard infantryman. Many people (including in this thread) incorrectly generalize this to all horses in all armies. Steppe ponies require substantially less food by weight than a Central European draft horse (a true chonker of a horse!) and both are different in veterinary and shelter requirements as well (steppe ponies are much more resilient to weather than a Central European draft horse which requires a regular stable). Central and Western European officers have historically had immense difficulty grasping this point
* horses are dramatically less resilient than men to exhaustion and interruptions in supply. While a man can go seven days without food before suffering severe health consequences a horse is typically doomed to die after three.
* mobility. While light cavalry can typically go most places -- and mules can go anywhere a man can, making them still the premier choice for supply in high altitude environments -- heavy cavalry is constrained to operating only in open terrain with some fairly strict limits on ground state and terrain complexity. A big, heavy and potentially armored horse carrying a big, heavy and heavily armed and armored man is simply not able to cross a muddy field, river or complex terrain more generally
* water transport. Horses cannot safely be transported any great distance by sea without loss rates in excess of 70% (yes, really, even 100% loss rates are considered unfortunately but fairly typical) unless special accommodations are available. And by that I mean purpose built ships with special harnesses to suspend the horse in mid air. Horses panic in even mildly challenging sea state and have a tendency to badly injure themselves with panicked kicking. Here is a broadly accurate depiction of the British method of horse transport
Elephantery and Camelry have similar limitations but with some special twists. Elephantery's command and control challenges are well known, but the veterinary and especially nutritional requirements are if anything an even more insurmountable challenge! Not to mention elephant stud farms are quite challenging to build and so expensive that only a few states have been willing to maintain them for any length of time. Almost all nations abandoned elephantery as a concept relatively quickly. The sole exceptions are South East Asian states where elephants are nigh omnipresent and even there they were primarily used as an elite status symbol, not a primary combat arm. Camels are extremely good in their preferred desert operating environment and are the premier animal for long distance desert maneuver but lack the speed, strength and stamina of the horse and in terrain that isn't desert struggles to match their equine competitor in any aspect. They also happen to be... unpleasant companions. Where the horse tends to compete with the dog for the status of man's best friend... the camel is in contention with the cat for man's least agreeable companion.
So if I were going to modify cavalry to appropriately depict them and their historical limitations
* heavy shock cavalry should outperform infantry in open terrain, no question. The bonus should NOT be small! Think +5 or even +10
* heavy shock cavalry should not be able to fortify. Cavalry have to keep their mounts alive. This is no small task. They don't have time to waste on digging. Digging is the domain of the poor bloody infantry!
* heavy shock cavalry should have a baseline doubled flanking bonus. While they were perfectly capable of smashing infantry formations with a frontal charge whatever the claims of the "horses too scared to charge formed infantry" lobby -- despite the innumerable records of horses doing exactly that, including modern footage of horses charging large blocks of protestors.... or the fact that in the Macedonian system the cavalry was the decisive arm that shattered the phalanx of the enemy while the phalanx existed merely to fix the enemy in place for the killing blow -- the preference for the cavalry has always been to hammer the enemy after they have been worn down by the infantry as this permits the desired decisive blow
* heavy shock cavalry should have a HP replenishment penalty of 5. This means they would not replenish health in enemy territory without an appropriately promoted logistics general
* heavy shock cavalry should have a combat penalty in all non open terrain unless an appropriately promoted maneuver general is supporting them
* heavy shock cavalry should not be capable of ocean transport until the modern era (yes really, horse transports were a fairly late innovation. some horses made it over the ocean to the Americas but formations of heavy shock cavalry absolutely not)
* heavy shock cavalry should have high maintenance cost
It would be good if an explicit light cavalry branch was added that included but was not limited to horse archers. This formation would operate similarly to infantry -- including the option of ocean transport -- but with better vision range and better mobility. Their primary use case would be reconnaissance, screening, and escorting generals, settlers and the like high value targets. You wouldn't want to use them for direct combat and they wouldn't be particularly good at it, but they'd be a great tool for grabbing terrain, watching flanks and generally being the eyes and ears of the commander.
Summarizing the intended roles:
* heavy shock cavalry would be the premier high power tool in the field but lack the replenishment capability and defensive capability to match infantry in sustained combat. If you see a maneuver general with a packed blob of heavy shock cavalry, you should be deeply concerned
* infantry would dominate rough terrain and siege warfare by virtue of their ability to replenish more quickly and to dig in
* infantry would be the preferred tool for expeditionary warfare as unlike cavalry they would be sea transportable