Seems Roman Catholicism has set up yet another "tradition" not substantiated in Scripture.
Roman Catholicism can do what it wants...it's just there is no Scriptural prohibition against a regular person reading the texts aloud in church.
Scripture is not being read "in public".
The Gospel (i.e. a reading from one of the first four books of the New Testament) is being proclaimed as part of the Sacred Mysteries; what we call "the Mass" or 'the Holy Sacrifice" and the Orthodox call "the Divine Liturgy". This is celebrated by a priest who is ordained to offer the Sacred Mysteries.
Catholics are as free as anyone to read the Gospel "in public".
Different religions have different rules. You are not Catholic and don’t wish to be, which is fine.
We're not talking about "reading Scripture in public". We're talking about proclaiming it liturgically to the assembly at Mass. There are rules and commands in the Bible about worship being done in an orderly fashion, aren't there? There are in my Bible.