Stationary archers can shoot farther and stronger bows than horse archers. A horse wouldn’t charge a spear and gore itself so why couldn’t regular armies just use a lot of archers and piles/spears to beat steppe armies? How would steppe armies even begin to beat such a force?
Well of course you're right, steppe armies cannot hope to defeat a stationary force of infantrymen armed with bows to respond to arrow fire and walls of spears to defend against enemy charges, not only that but they might just be more numerous since agrarian empires have much more resources at their disposal to equip greater amounts of troops, and might be better equipped too. So you're definitely on point, steppe armies would definitely be defeated in a pitched battle by a regular army.
That's exactly why they wouldn't fight such a pitched battle
The strength of the steppe armies is on their strategic and tactical mobility, which gives them the initiative over their much, much slower sedentary enemies. When the agrarian armies are on the offensive, the problem is that a big infantry army is not only slow because it moves on foot, but because these soldiers need food to survive, and fighting against steppe nomads you're not gonna find the rich agricultural lands to live off of like you would fighting your farmer neighbors, so you have to rely on wagon trains carrying food and other supplies for the army to traverse the inhospitable steppes. Of course the animals that haul the wagons also need fodder, which adds to the load, and also remember that you need to pack food for the journey back as well, so you need a disproportionate amount of wagons for your army to survive when campaigning against the nomads, and the end result is that your army moves at snails pace, which couldn't possibly be worse when fighting against an enemy that not only fights but quite literally lives on horseback. The steppe nomads need not face this army in a frontal battle, that would be ridiculous, they instead rely on their mobility to defeat this bumbling giant, effectively by denying them a decisive encounter of any kind, they will harass and skirmish with the slow moving columns, pick on units that straggle too far away or foragers looking for fodder, attacking their supply wagons and rearguard, and luring the enemy into ambushes. If the enemy reaches the place that the nomads live in, then they will be shocked to find that the cumbersome dependence on land that defines the agrarian societies does not bother them, they can just pack up and move further into the steppe, they are used to that anyways. Then the equally slow and disappointing journey back will be made a tormenting experience by the now pursuing nomads. In Chinese history for instance it was only when the empire was at its strongest, during the Han, Tang or Ming dynasties for example, that it was able to sustain these insurmountably costly expeditions against the nomads.
When on the defensive the agrarian societies don't fare much better, because they won't face a single, relatively slow moving army moving along a predictable path (Hannibal's crossing of the Alps for example was unexpected to the Romans because of the tremendous logistical hassle that taking such a path would have entailed, especially with elephants), they will instead have to fight an authentic swarm of fast moving raiders attacking over a wide front, swiftly coming, laying waste to the countryside, and quickly vanishing back to the steppes. Organizing an effective defense is similar to the above a tremendous logistical expense, for a number of strategic and mutually supporting forts have to be constructed and frontier units have to be stationed to be on guard at all times. The great wall of China is only the most well known example of this, and bear in mind that it was not just a big wall to keep raiders out, it was more of an early warning system for frontier troops to be able to quickly raise an alarm that an attack was going on for the main garrison troops to mobilize against the threat. A similar system of southern fortifications created by the Muscovites did not however stop the Crimean Tatars from razing Moscow itself in 1571.
The above is rather facetious actually, the steppe nomads did fight pitched battles, they were after all fearsome warriors fostered in a dedicated military culture, born in the saddle and beyond proficient in the use of the bow, accustomed to internecine warfare amongst themselves. But because they had the strategic initiative, they would only fight a pitched battle if and only if they had the advantage, that is, they would only fight an enemy after it was tired, hungry, disorganized, and not really expecting a battle. Even then they would not rely on a frontal charge, they would rely once again on their mobility and superior discipline and cohesion in order to attack the flanks and rear, defeat the enemy in detail, or the most iconic of all performing a feigned retreat, in which they would harass the demoralized enemy formation with showers of arrows, and provoke them into charging, once they did they would pretend to rout, which would then prompt the enemy to follow in hot, disorganized pursuit, only to fall into a surprise attack as the nomads wheeled about to counter charge, or attack the flanks, or attacking with a concealed force, or in the age of gunpowder luring them into their own prepared positions to blast at them with murderous cannon and musket fire. Several battles throughout the ages played out this way, Carrhae against the Romans, Manzikert against the Byzantines, Hattin against the crusaders, Kalka against the Rus' princes, Sarhu against the Ming, heck the Mamelukes pulled it on the mongols themselves at the battle of Ain jalut!
So pitched battles were actually dead last on the list of agrarian societies for dealing with steppe nomads, the best ways were employing fast moving cavalry with little logistical needs themselves, either trained by themselves or recruited as mercenaries from the nomad populations, relying on defensive fortifications as mentioned, since steppe nomads aren't particularly adept at siege warfare, and diplomacy, either by appeasing the nomads with marriages, tribute and trading rights or by pitting different tribes against each other to keep them busy and keep them from coalescing into a stronger political entity. When on campaign then indeed heavily armored infantry supported by archers, crossbowmen or musketeers, and often using their supply wagons as mobile fortresses, were very effective, but would be useless without supporting cavalry and would also be useless if the nomads decided to not attack at all or could not be lured into doing so
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There's always more that can be said, but you might enjoy this recent answer from /u/Wotan_Weevil that touches on a similar topic.