Not really familiar with the middle ages in terms of campaigns, but I have some familiarity with ancient warfare.

Sieges in general tended to be very costly during warfare and a time wasting avenue. Depending on how well fortified a settlement or a fortress can be, you could take months or even years and a siege would mostly end up just standing around a city waiting for something to happen. Even worse if that city is close to the coast and can be supplied by sea.

Imagine if there were at least 20-30 forts or even more well fortified cities, there were a lot of fortresses and cities you have to pass in order to advance deeper into enemy territory. Usually it isn’t recommended to leave enemy fortresses and cities behind the army as that will expose them to harassment from the sides or rear. Small skirmishes that slowly chip away an army’s ability to fight. Any foraging party would be ambushed and destroyed in small skirmishes. A couple hundred or thousand depending on the scenario.

You are mostly correct in saying that pitch battles don’t tend to happen a lot. Though I think that people have this misconception of pitch battles being too scarce.

For one, we’re relying on written sources most of the time in order to determine how much pitch battles were conducted. This means that we usually don’t get a clear picture as to how many times it really happens. Or how many that actually did happen occur. Some time periods remain obscure and have lack of written sources that clearly portray events accurately. Some sources go so far as to “mention” a battle but glossed over such events.

The late roman period have huge amount of sources in the 4th century, but the 5th century has
very few written records to depict this period. We have a general idea of what happened during this period of strife and unrest but times can be quite chaotic that there just aren’t that many written records. Archeological record is even harder to find. Some findings by historians in Europe tend to be in a different language. Roman artifacts can be found in many places in Europe. Not all of them are translated however and its usually time consuming to translate those works. There is also political quagmire to get those works and publish them.

That said pitch battles happens under specific circumstances. The enemy has a huge force and you need to overwhelm them while morale among your soldiers are high in order to capitalize on the fact that the enemy is grouped up together tightly and engage while they are all in one place instead of spread out over a large area in small parties.

For instance, we can use Julian’s campaign in gaul mentioned by Ammianus Marcellinus in the 4th century. The germanic tribe confederations of the Alemmani and Marcommani and several other confederations of combined tribes attacked Roman Gaul and completely overwhelmed the entire province. Sacking various cities and settlements. Some reaching quite close to Italy.

The breached frontier needed to be reclaimed. Gaul served as the primary recruitment drive of most of the Western Roman army since its administrative split with the east. The second one comprised of regions of Hispania and Iberia.

Germanic confederations of multiple tribes demonstrated that many of them were becoming much too strong and were getting more aggressive against Roman frontiers ever since the late 2nd century.

Julian’s move against the Germanic tribes is to capture back the region and bring it back under Roman control. Various minor battles were already occurring between Roman troops and germanic soldiers.

Julian led by example. A typical bookworm that was considered a decent Caesar by Constantius II to govern the west at the time. Constantius was a bit of a paranoid men and had murdered much of his family in a bitter power struggle to get the throne. He became Augustus of the the entire empire but allowed some degree of autonomy to Julian considering that he wasn’t much of a threat to Julian at the time.

Julian studied history and battle tactics of previous emperors and led successful campaigns against the germans using tactics of his predecessors. Influenced by the likes of Alexander III he inspired his troops but was hamstrung by internal corrupt bureaucracy. Several officers were suspected to be sent by Constantius to keep watch over the young Caesar. Several of them led their troops back to Mediolanum to their winter quarters and abandoned the campaign leaving Julian with a meager force of around 15,000 men.

King Chnodomar the leader of the germanic tribes sought to wipe out Julian’s force now that it had reduced to a smaller force. His forces supposedly numbered 30,000. He summoned back the raiding parties to group up. Julian was camped in one of the local abandoned cities and was informed of the presence of the german army nearby and wanted to avoid battle first as it was closing night time as his troops needed rest. His troops refused such an order and all clamored to engage Chnodomar arguing that now the enemy were all grouped up together, they could defeat them in one fell swoop ending the campaign while their morale were high. Julian’s officers also encouraged Julian to engage. Julian decisively defeated the germans at Strasbourg in 357 AD.

Several more conditions are needed to engage in a pitch battle. Accident. Sometimes both armies accidentally engaged one another. For example, foraging parties of both side engage in a minor battle by accident due to thick fog and huge ridge lines. They then send parties back to both camps respectively to inform their generals that they need help. Both generals send more and more to reinforce and then quickly form up both armies to engage. Such an event happened during the battle of Pydna between the Roman republic and the Macedonic kingdom.

Or sometimes the enemy are just too large in force and you need to destroy them before they became too huge. If a general avoids battle he can be seen as a coward from his troops and can be potentially assassinated for cowardice. Many soldiers defend their own frontier towns and had settled families in the region. To avoid battle is to put their families at risk. Large scale mutinies among troops who felt their families were ignored can be very dangerous. Indeed generals can be forced to fight in a pitch battles by their own troops. Local politics also play a part.

If the people are angered by the lack of governmental efforts to destroy the invaders destroying the countryside, they could rebel against their rulers who they saw as negligent in their duties to protect the lands from being destroyed. This is why scorched earth or delaying tactics by rulers are incredibly unpopular. Farms and towns destroyed. Food such as cattle are taken by the invaders. This can destroy a ruler’s reputation and paints him as someone who can’t protect their people. This is something the opposing army can take advantage of. This is why pitched battles can occur more quickly than what is typically portrayed. Pitched battles less commonly but are not super rare as one might think. Just not very common.