Indeed, the generals would likely end up going after the Imperial throne like popular Roman generals often did. The first one to succeed would probably also immediately scrap the whole election thing.
IIRC the Han dynasty imperial bureacracy ceased to exist below the Xian (county) level, so areas of ~2000km² & 30-40000 people (probably at least double that by the time of this Zhou dynasty). So any dispute over a few cows would be handled by the village elders.
That is actually not correct for Han dynasty.
The Donghai commandery reports mention 2202 or 2203 officials in an area with 1,4 million people. A lot of them were "ting zhi" - apparently formally appointed officeholding village clerks, though the terms of their recruitment and remuneration is not clear to me. There also were township levels, and township level clerks.
Han dynastly had a total of some 130 000 officials.
There was some distinction between the mass of lower officials and middle/higher level officials, but the formal reports grouped both together.
In the Song, Yuan, Ming and Qing dynasties, clerks ("li") continued to exist in large numbers - but the distinction between clerks and mandarins ("guan") strengthened. The histories seem to report number of mandarins alone, omitting clerks, and it sees that by late Ming the government had lost track of how many clerks there were - true number of clerks was no longer reported.
This development, however, happened in fits, starts and reversals.
By 1600, China had an unknown number of clerks, but probably over 200 000 - over 100 clerks per county
By 1600, China had around 500 000 "scholars" ("shengyuan"). So around 400 scholars per county.
But importantly, these two groups, in OTL Ming and Qing, had minimal overlap, and rivalry attested even since Han. Under the Ming-Qing rules, the clerks were formally barred from taking exams. A modest number of scholars took employent as clerks, but this entailed permanently giving up the status of scholar.
Since the 500 000 scholars were recruited by exams, and several times that number took the exam, repeatedly, it was logistically feasible to hold the exams for shengyuan status (at prefecture level).
Which means it could have been feasible to recruit clerks by exams - testing not mainly Confucian classics, but practical literacy and numeracy.
There were political reasons why Ming did not, but another regime might.