It is clear that almost no denomination obeys the Scripture illustration, which is once, each week, on the first day of the week, when the whole assembly gathers, to which all of its constituents are assembled for worship and collection of contributions to the ministry.
There is no worship without (a) sacrifice(s); of which the Remembrance Supper portion (in which we bear his reproach, Heb. 13:13, by showing forth His Death till He come, 1 Cor. 11:26, and identifying with him by figuratively eating/drinking the tokens of His shame) is one, the fruit of our lips giving praise to His Name (Heb. 13:15) is another, the offering of tithes and gifts (which is "communicating", Heb. 13:16b) is yet a third, and lastly the going forth to accomplish good things (Heb. 13:16a) for the coming week which concludes the regular summons to assemble.
The only manifestation I have seen regarding this is evidenced in the meeting of local Christian brethren after the Scriptural pattern of Darbyites, loosely known as "Plymouth brethren."
All Romanists, nearly all Reformants, and most Rebirthers get it wrong, IMHO, and do suffer from it for their lack of discernment (as well as allowing unregenerates and/or unconfessed constituents to partake).
Though I agree with you about many points, I do not on this topic. Whatever Scripture "illustration" we are given about the remembrance of the Lord's Supper, nowhere is the frequency commanded. Paul said in I Corinthians 11:25-26,
In the same way, after supper he took the cup, saying, “This cup is the new covenant in my blood; do this, whenever you drink it, in remembrance of me.” For whenever you eat this bread and drink this cup, you proclaim the Lord’s death until he comes.
I believe Paul's rebuke of the Corinthians was their coming together for "love feasts" (which was a communal "covered dish" type of activity) and was done to ensure no one went hungry among their fellowship. That's why Paul said if they were so hungry they couldn't help butting in line and gobbling up the food and wine (getting drunk in the process) so that others went without, they should eat before they got there. This denotes, to me anyway, that this was not the same thing as the Lord's Supper observance where a loaf of bread was passed around, each person breaking off a piece, the cup passed around for a sip and the words of remembrance for which this ordinance was done spoken by the leader of the local church.
As is the same issue of what day(s) of worship are and what feast days and sabbaths are set aside, Paul said each man must be fully persuaded in his own mind because it is between him and God:
Who are you to judge the servant of another? To his own master he stands or falls; and he will stand, for the Lord is able to make him stand. One person regards one day above another, another regards every day alike. Each person must be fully convinced in his own mind. He who observes the day, observes it for the Lord, and he who eats, does so for the Lord, for he gives thanks to God; and he who eats not, for the Lord he does not eat, and gives thanks to God.… (Romans 14:4-6)
We have liberty in these areas and in others, such as food sacrificed to idols, from blood, from the meat of strangled animals and from sexual immorality (Acts 15:29) as well as the major tenets of the Christian faith, we should be obedient and in unity. There is no mention from the Apostles about how often the Lord's Supper observance was to happen - not even the precise day of worship - as the times they lived in getting together on a regular basis may have been difficult. Though we do know that the early church gathered together on the first day of the week in several references and also some writings of early Christians regarding the process of their worship time.
Those are my thoughts anyway. Have a good night.