I’ll speak mainly to the Buddhist tradition but I can also give a little bit of insight into the Christian side as well.

The short answer to your question has to do with asceticism and the way it developed in South/East Asia and the West that encouraged monastic forms of asceticism. That can also lead you to the answer as to why monastic asceticism is not as prevalent in other teachings like Daoism and Islam where asceticism is also present.

In Buddhism, group ascetic practice actually predated the Buddha himself as the story goes he sought instruction on suffering from an ascetic lifestyle. However, after Siddharta Gautama’s enlightenment, he also codified this lifestyle in his teaching, drawing together followers and encouraging them to form a mutual association based in shared behavior, belief, and most importantly, strict subscription to a rigid lifestyle. This group is called the sangha, which in a strict definition of the term refers to the monks and nuns who take on this lifestyle. In loose definition (which is also validly used in some traditions), sangha can refer to the Buddhist community in its entirety. So, in some respects, especially with its provenance directly connected to the teachings of the Buddha of this age, monastic life was built right into Buddhist teachings.

———— Cf, Donald Lopez Jr., Buddhism in Practice, Princeton UP, 1995. This book gives a good all round introduction to Buddhism. ————

As Buddhism migrated to China after Siddharta’s parinirvana (breaking of the wheel of rebirth and entrance into nirvana upon his death), monasticism was retained, especially in areas like Dunhuang where monks congregated to pray and rich patrons would commission cave paintings to achieve merit. Whereas the ascetic lifestyle continued, Dunhuang is a good example of a cenobitic (community oriented) sedentary lifestyle where the Buddha and his followers would often travel to different places. Communities like Dunhuang on the silk route trading network were instrumental in transiting monks and texts from India into China during the first centuries after the Buddha’s death (Buddhism entered the Han empire proper in the second or third century CE according to physical evidence). The number of monasteries increased in China until an imperial proscription on foreign religions in 845 wiped out a lot of landed monasteries (think the appropriation of Templar resources if you’re familiar with that) and it would take a while to bounce back while less-sedentary and cenobitic sects like Chan/Zen survived.

One of the politico-religious reasons for that proscription had to do with Daoist influence on the emperor of the time, the Tang Emperor Wuzong. While asceticism existed in Daoist circles as well, both religions possessed elite connections that allowed them to lobby the imperial court depending on which way the wind was blowing at the time. Wuzong’s proscription of foreign religions forced many monks and nuns to return to lay life and see the confiscation of temple grounds (and thus, assets) by imperial officials. I should note here also, that one aspect of difference between Western and East Asian monasteries is their locations. Monks lived and were/are responsible for temples in urban areas just as in rural and this continues to the present. My understanding of the Western trend is that monasteries were decidedly rural for the purpose of isolating oneself/the community from the profane. Chinese monks, in my knowledge, did and do perform spiritual tasks for visitors and this supply income for the temple/monastery. There are of course exceptions to this as mountain monasteries are very prevalent (think N. And S. Shaolin, or the aforementioned Dunhuang), but the existence of monasteries in the hearts of cities should not be ignored.

————— Cf, Erik Zürcher, The Buddhist Conquest of Asia, Brill, 1959 & 2007. This is a must-read for the development of Chinese Buddhism

Jacques Gernet, Buddhism in Chinese Society: an Economic History from the Fifth to Tenth Centuries, Columbia UP, 1995.

Susan Naquin, Peking: Temples and City Life, U California Press, 2000.

Michael J. Walsh, Sacred Economies: Buddhist Monasticism and Territoriality in Medieval China, Columbia, 2010. (Big thumbs up to this one) ——————

This section will be shorter, but on the Christian side of things, in comparison with Buddhism which is the spirit of your question, the monastic community began to emerge only in the centuries after the Resurrection. At that, the form of asceticism that these early monks (like St Anthony of Egypt) practiced usually followed an eremetic (think hermit) path versus a cenobitic one. Here, the common denominator is asceticism, just the form differed. In the West/Mediterranean, the first movements toward Christian asceticism was isolated and eremetic. Later Christians would also develop cenobitic forms that pretty closely mirror the Chinese Buddhist format. (I should add that there were also itinerant monks in Asia, too. The first Ming emperor spent part of his youth as an itinerant novice wandering China.)

Historian Marilyn Dunn is well-known for work discussing the histories of both male and female monasticism in Europe. I know she has a chapter that discusses St Pachomius (I’ll put it below), but you’ll also want to consider the Benedictine order—the rule of St Benedict.

I won’t comment on Islam as I don’t know enough about it other than to direct you to Sufi mysticism as a potential starting point for Muslim asceticism.

———— Athanasius of Alexandria, Life of Anthony of Egypt

Marilyn Dunn, The Emergence of Monasticism: from the Desert Fathers to the Early Middle Ages, Blackwell, 2000. ————