You are arguing from silence.
Unfortunately everyone is arguing from silence; or at least the ones who are ignoring the cultural setting of the Archaean Christians and the many other cultures of the Mediterranean region are doing so.
There is no evidence whatsoever to support your claim that the Corinthians met in such places.
Why should the various congregations within Archaea (Corinth, Lechaion, Isthmia, Cenchrea etc) be any different to all those other churches who reside in climates that encourage open air meetings; after all, even John the Baptist regularly held large outdoor baptismal meetings and Jesus held open air meetings in Israel on the side of hills where over 5000 congregated and these meetings were at times kilometres away from town or village centres. We should also include the discovered towns/communities of Sicyon, Phlius, Cleonae, Examilia and Cromna which were all within a 10km radius of the centre of Corinth.
As the culture of the various Mediterranean societies was and still is heavily based around open air family and social gatherings, then I cannot imagine why the various Churches within Archaea of Pauls day should be any different. To attempt to say that the Christians of Archaea were different to the rest of their culture along with the numerous other cultures around the Mediterranean is based on desperation and not reason.
For that matter, why should the Christian community who had as one of its member/patrons, Erastus, who was the city treasurer or works manager feel that they could not on the occasion use the theatre which is in the centre of the city or with the Amphitheatre on the Northern part of the city, particularly when Erastus figuratively held the keys to these buildings.
Then we have the question of baptisms, weddings, funerals and other family events that many within the various Achaean/Corinthian communities would desire to attend. Where would these people meet, in a single home or in a venue that was capable of assembling the who knows how many potential Christian friends and family members all at once?
Street evangelism links
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We know for a fact the Corinthians met in people's houses.
We certainly know that some of the congregations within Achaia meet within houses, but when Paul or anyone refers to someones house, this also includes their open air gardens and fields as well, so a large meeting of several hundred could easily be held in the open within a private residence/property. Even today in many larger and sophisticated regions in the West, there has been a tendency for a number of years for many to hold weddings and other large family social events in the open where they can be away from buildings and enjoy the surrounding vistas; as Greece has been known for this lifestyle choice for centuries then why should the Christians in Achaia be any different. For that matter, unless the weather around the often balmy Mediterranean was wet and cold, why would any group of individuals want to sit inside if they had the option of meeting within a pleasant garden setting?
With the house churches that Paul speaks of, they were the ones who contained his personal friends and associates, where there would have been quite a few congregations/house churches that Paul had never come across. It should be noted that as Paul had many apparent enemies within some of the Archaean congregations, which included the Peloponnese Peninsula, the Corinthian Isthmus and much of what we know as Southern Greece (2Cor 1:1), then he would be unlikely to pass on any possible greetings from those who opposed him.
There is no mention of them meeting anywhere else, even when they they joined together. Even if they did meet in open fields the person speaking in the unfamiliar tongue would only have been heard by those immediately surrounding him, so your argument still doesn't stack up.
Why would Paul want to record where all of the individual congregations met and when – who would bother to do such a thing especially as First and Second Corinthians and his visits covered a six year period from his founding of the Churches in Corinth? As Jesus was able to address crowds of 5,000 in the open then why should it be a problem for a speaker to be heard by a group of a hundred, several hundred or even a thousand or more? Don’t forget, we are not talking about the Upper Northern hemisphere with its ice and cold winds but with the balmy and moderate Mediterranean world.
For that matter, to my knowledge Paul does not speak of any Christians paying rent or that they went to the numerous public plays in the various amphitheatres, so should we presume that they did not pay rent or go to plays? Paul certainly does not make any reference to their private ablutions but archaeology has uncovered many sophisticated public toilet cisterns in numerous Roman cities, does Paul’s understandable silence on these matters mean that Corinthian Christians never used a public bathroom/toilet or that they never even took a bath?
Your suggestion that the total number of Christians in the area ran into the thousands is laughable. The scholars agree there were only 50-100 or so in Corinth, the main town of the area. Cenchrea, Lechaeum and Isthmia were much smaller in size. So the total for the entire area would have been no more than 100-200.
As to “The scholars agree”, about the only person I know of who has dared to make an assessment on the size of the Corinthian church/s has been the recently deceased archaeologist-historian Rev. Prof. Jerome Murphy-O’Connor with his notorious “40-150” persons which many others have seen fit to refer to, as per below:
www.bibleodyssey.org
“It is difficult to know the size of the Corinthian church at the time of this first letter. Scholarly estimates range from 40 to 150 persons. It is often assumed that when “the whole church” came together for worship (1Cor 14:23), it did so in a believer’s home, but Paul’s distinction between church and home in 1Cor 11:22 may suggest otherwise (compare 1Cor 11:34, 1Cor 14:34-35). The meeting place may have been a rented dining hall, a large garden, or some other venue”.
link
The above comment on Paul’s use of
church and home is important as it shifts the emphasis away from the mere walls of a given home, where it could also be in a large rented venue and the “large garden” could be in a patrons private garden or field or a public space which Jesus himself utilised at times.
As to the Evangelistic efforts of some of the most powerful ministries of the First century within the Achaean region, it is hard to imagine the
signs and wonders ministry of Paul and probably Barnabus, along with the powerful ministries of Apollos and the other renowned individuals of the the day only achieving a result of "40-150" persons; though I could certainly agree with a figure of at least 40-150 congregations within Achaia.