When these letters were written the "dioceses" were just taking form but the warnings were for those that had come together,taught by one of the "apostles",or sent by an "apostle" to work out how to achieve the great commission,"to baptize in the name of the Father,Son and Holy Ghost and teach all nations what He had taught them".
One of the teachings that was to be passed on once the door was opened to all was that Jesus was "the Way,the Truth and the Life" and man had to accept that in order to benefit from the salvation which was offered to all.In todays language that might be the cost of oppurtunity.To "overcome" one needed to believe that He was the Way,the Truth and the Life".So one needs to start around the time Jesus's public ministry started,about the time He "overcame"the temptations of the world,the flesh and the devil.
I always thought that the salvation offered was the opening of the door to "eternal life" which had been closed to all but the "chosen" until He came.
"For us men and for our salvation,He came down from heaven,and by the power of the Holy Spirit,He was born of the Virgin Mary,and became man".
So it looks to me like salvation is a open to all but "eternal life" is contingent on our cooperation with the grace God gratuitiously showers on us. The warnings to the churches were pointing out the areas where the temptations of the secular world were inhibiting both individuals and the "body of believers" to "overcome".
Today the Pope could write similar letters to bishops of dioceses who are failing to "overcome" and list the areas of weaknesses and strengths.God in His mercy sent His Son to open the door for all,which He did by establishing a Church.Man,who by his nature wants to name good and evil and yet attain heaven,from the get-go,disobeyed by failing to "overcome" the seduction of the serpent. Twas ever thus,for most.