Much more can always be said about this, but I answered something similar in the past, which may be helpful:
(Short answer - yes, some kings did this for their aristocratic entourage, but probably not really for peasants)
It may be more a trope than a common practice, but there were cases of such behavior. During his reign, Habsburg emperor Joseph II made dozens of trips solo or with a small entourage all over his domains. He famously made a point to set himself in any village or town with a desk to receive written petitions from anyone for any reason. Requests for money were rejected and burned, but he was especially receptive of complaints about local governors and the like. The picture we have of him from his letters and proclamations is of a rather quixotic ruler obsessed with micromanagement and distrustful of subordinates, who ultimately wore himself out and died early.
My sense is that having a reputation as a ruler that receives petitions from the peasantry was considered a very good thing, though not practiced in reality by most monarchs. Receiving serfs could also mean undercutting the authority of one's own feudal subjects, arousing aristocratic opposition.
After his death, Joseph was apparently remembered fondly in parts of Bohemia as an active ruler who sponsored agriculture and development. He was much less popular among the the Viennese aristocratic bureaucracy, and even acquired a tyrannical reputation among the Hungarian patricians for other reasons.