Many have a defective Ecclesiology today, even in Reformed churches. The sacraments are given to the church, not to individuals or families. WCF XXV:iii:
Unto this catholic visible Church Christ has given the ministry, oracles, and ordinances of God, for the gathering and perfecting of the saints, in this life, to the end of the world: and does, by His own presence and Spirit, according to His promise, make them effectual thereunto.
The Westminster Directory for Family Worship provided safeguards against family worship being regarded or replacing authorized public worship:
III. As the charge and office of interpreting the holy scriptures is a part of the ministerial calling, which none (however otherwise qualified) should take upon him in any place, but he that is duly called thereunto by God and his kirk; so in every family where there is any that can read, the holy scriptures should be read ordinarily to the family; and it is commendable, that thereafter they confer, and by way of conference make some good use of what hath been read and heard. As, for example, if any sin be reproved in the word read, use may be made thereof to make all the family circumspect and watchful against the same; or if any judgment be threatened, or mentioned to have been inflicted, in that portion of scripture which is read, use may be made to make all the family fear lest the same or a worse judgment befall them, unless they beware of the sin that procured it: and, finally, if any duty be required, or comfort held forth in a promise, use may be made to stir up themselves to employ Christ for strength to enable them for doing the commanded duty, and to apply the offered comfort. In all which the master of the family is to have the chief hand; and any member of the family may propone a question or doubt for resolution.
IV. The head of the family is to take care that none of the family withdraw himself from any part of family-worship: and, seeing the ordinary performance of all the parts of family-worship belongeth properly to the head of the family, the minister is to stir up such as are lazy, and train up such as are weak, to a fitness to these exercises; it being always free to persons of quality to entertain one approved by the presbytery for performing family-exercise. And in other families, where the head of the family is unfit, that another, constantly residing in the family, approved by the minister and session, may be employed in that service, wherein the minister and session are to be countable to the presbytery. And if a minister, by divine Providence, be brought to any family, it is requisite that at no time he convene a part of the family for worship, secluding the rest, except in singular cases especially concerning these parties, which (in Christian prudence) need not, or ought not, to be imparted to others.
V. Let no idler, who hath no particular calling, or vagrant person under pretence of a calling, be suffered to perform worship in families, to or for the same; seeing persons tainted with errors, or aiming at division, may be ready (after that manner) to creep into houses, and lead captive silly and unstable souls.
VI. At family-worship, a special care is to be had that each family keep by themselves; neither requiring, inviting, nor admitting persons from divers families, unless it be those who are lodged with them, or at meals, or otherwise with them upon some lawful occasion.
VII. Whatsoever have been the effects and fruits of meetings of persons of divers families in the times of corruption or trouble, (in which cases many things are commendable, which otherwise are not tolerable,) yet, when God hath blessed us with peace and purity of the gospel, such meetings of persons of divers families (except in cases mentioned in these Directions) are to be disapproved, as tending to the hinderance of the religious exercise of each family by itself, to the prejudice of the publick ministry, to the rending of the families of particular congregations, and (in progress of time) of the whole kirk. Besides many offences which may come thereby, to the hardening of the hearts of carnal men, and grief of the godly.
Historic Church Documents at Reformed.org