Update: I have become increasingly convinced that Christ and the Father want the absence of hierarchy among the disciples, especially based on Christ's words in Matthew 23 and John 21. The Lord Jesus is recorded as saying in Matthew 23 that all disciples are siblings, none of whom should be called rabbi or guide, because we have one teacher (the Christ), and that anyone who exalts themselves will be brought low. In John 21, the Lord's commission to Peter can be read without any permission for hierarchy: the two Ancient Greek verbs used there, bosko and poimaino, had several senses each, such as "feed" and "tend" respectively.
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House churches are a sound way to organise Christian life, as long as the other governance structures that the Bible describes are also applied: properly qualified elders/overseers [1] who are rewarded according to performance [2], and evangelists whose responsibilities include refuting false teaching [3].
References
[1] "It is necessary, therefore, the overseer* be blameless, husband of one wife, sober, sensible, well-ordered, kind to strangers, apt to teach, not tarrying at wine, not a striker, instead reasonable, not battling, not a lover of money, leading his own household well, having children in obedience with all reverence (yet if someone does not see to lead his own household, how will he manage God's ecclesia*?), not a neophyte, so that he not, having been deluded, fall into the Devil's judgement. Yet it is necessary to have a good testimony from them outside, so that he not fall into reproach and the Devil's snare." (1 Timothy 3:2-7, CFB)
"For this grace I left you behind on Crete: so that the remaining things you would set up rightly and appoint by city elders, as I ordered you, if someone is blameless, husband of one wife, having faithful children not under accusation of wastefulness or unruliness. It is necessary, indeed, for the overseer to be blameless as God's house-manager, not self-willed, not inclined to wrath, not tarrying at wine, not seeking shameful gain, instead kind to strangers, loving what is good, sensible, just, holy, controlled, holding before himself the word of faith according to the teaching, so that he be able both to appeal by the instruction that is sound and to refute them speaking against it." (Titus 1:5-9, CFB)
[2] "The elders who are leading well must be deemed worthy of double honour, especially they who are working with the word and teaching. For the Scripture says, "An ox treading you shall not muzzle", and, "Worthy is the worker of his wage." (1 Timothy 5:17-18)
[3] "Trustworthy is the word, and I want you to be thoroughly established regarding these things, so that they be minded to stand over good works, they who have been trusting God. These things are good and profitable for all human beings." (Titus 3:8, CFB)