Actually, cavalry could be demonstrated redundant in one area while remaining useful in another. While it was still used as a combat arm, it had a valuable reconnaissance function as well as increasing communications when the horse is the fastest way of transmitting a message - though bicycles were spreading. Even the Belgians had a bicycle battalion in their cavalry division in WWI. If you had a large die-off of horses (didn't Ward post a scenario based on this in ASB or pre-1900 once?), then you'd see them replaced with something else.
Ah - the communications utility of the horse is something that is secondary to it's main cavalry role. Horses need food, water, stable hands etc... something not needed with bicycles. Recon by early balloon, biplane etc was also reducing the role of the horse. Not that horses are redundant... just their role is diminished. Horses were still used to haul guns and transport goods via wagon train.
Conceivably an earlier/more widely produce/better machine gun would have led to an interesting change of tactics. Make it light enough to put on a horse, carry the tripod and ammo on yet anoher horse... maybe a group of 6 horses for 2 machine guns. Put a mortar on a 7th horse, and the ammo on an 8th. Suddenly you have an 8-man 8-horse squad able to move rapidly, attack from a distance with a mortar and a pair of machine guns.
Standard cavalry wouldn't stand a chance, and their ability to move fast and bipass static defences make tranch warfare redundant. You now get a fast moving form of warfare where the ability to cover ground, set up your weapons and move on before the enemy can mount a counter-attack is far more important than having heavy guns to pound away at the enemy.
The role of static positions such as gun emplacements and trenches becomes redundant. You get tactics and units that rely upon speed and flexibility. Just as Hitler in WW2 completely bipassed the French defences, an enemy fighting these strike-teams would find themselves outflanked and cut off, then once lines of communication are down you send in the infantry to clear up the enemy using grenades and rifles. The cavalry would support this idea, as it keeps their position of prestige as an elite force.
Eventually in WW1, instead of the tank you'd see the development of lightly armoured rapid attack vehicles with mortars and machine guns, travelling in small squads. Something like a souped-up model T with larger wheels, or a Triumph trike?
"The Veloco... something?"
Hmm... "The Mechacav" ... Mechanical Cavelry
In this ATL we may see body-armour becoming heavier as these new mechanised knights need not carry their own weight. The members of a Mechacav squad would be able to rely upon cover less, but wouldn't have to carry their own weight (ie - less marching with packs), so we may see body-armour coming in a lot sooner. There was body-armour in WW1 & WW2 but the main point against it's use was that it was damn heavy and often saw the wearer taking a heavier wound from the shrapnel of the armour than the bullet would have caused itself. Conceivably you'd see 'heavy' squads with heavy body armour and 'light' Mechacav squads about... and some 'Heavy' squads would choose to ditch armour to gain speed/range/fuel_efficiency and some light 'squads' would add it. As the Mechacav evolve we'd see the armour moving from the individual to the vehicle (enclosed vehicles as opposed to open vehicles) and individual armour for the Infantry troops and the Mechacav members getting more similar as technologies develop.
You'd get a very different history of ground warfare. Tanks as we know them would (eventually) develop by WW2 but at first they'd be more like mobile emplacements, refueling their outrunning fast-attack-vehicles and mainly used offencively for long-distance shelling. They'd not be as heavily armoured as OTL tanks because they'd rely upon a squad fast-attack-vehicles for defence (and maybe squads stationed on them firing rifles), sort of like an aircraft carrier and escorting frigates.
Infantry would see body-armour a lot sooner, and with the faster Mechacav to cover ground the infantry wouldn't need to travel as fast and would be able to make use of the 'mobile emplacement' that is the centre of each formation to store armour on and take a rest on when the COs not looking.
Air warfare would develop in a similar way, but we may see ariel refueling a lot earlier to extend the range and mobility of fighters and bombers. I want to avoid saying 'zeplins' here because that is so cliche, but... zeplins.
If Hitler isn't butterflied away and we still get WW2 we'd end up with German rocket-trikes with huuuuuge inflated wheels (rubber+metal_mesh?) and rocket launchers thumping along, and improved British/American jeeps/landrovers with machine guns and mortars being the standard attack machine of the Allies. We'd still see tanks, but the emphasis will be on speed rather than armour.
By the late 20th century we'd see modern warfare being much the same, though with more 'humvee' type vehicles with mortars/grenade-launchers/machine guns/other and slightly less heavy armoured vehicles. The (fewer) tanks that we'd end up with would be bigger but less heavily armoured and with more emphasis on 'active' defences. We'd get heavily armoured foot soldier troops just as we do now, I don't forsee that we'd get power-armour by the end of the 21st century without some other changes so we'd see the Mechacav armour getting lighter and the Infantry armour getting heavier until you have a sort of standard armour system such as the ones employed by modern forces. Having said that the ripples caused by the earlier creation of the machine gun and the changes in history could see different military R&D priorities and I can certainly see that for urban warfare power-armour (that is to say very heavy power-assisted armour like a wearable super-light tank) supported by a squad of infantry would be mightily handy, as well as being something for dictators to spend their money on instead of large tanks.