There are a very few of us around here also, me included, who do pray a thanksgiving or other prayers after Mass, but I long ago taught myself to pray in the middle of just about anything, including the conversations of others.
Also, the churches are large enough that once the pews have significantly emptied, if somebody is chatting near me, I can easily move someplace else and other people who are praying will usually be doing the same, just moving to a quiet part of the church.
I have been in many churches where people will visit the statues of Mary, saints etc after Mass and say a prayer or light a candle; they all seem to be able to do that without being upset that a handful of people are having a brief conversation 20 feet away.
In any event, though, after Mass is not the time to settle down for a big holy hour with the Lord unless there is a scheduled activity like confessions at that time, or unless it’s a cathedral that is open all day, because after a short time then the Church is generally either locked up (and they will chase you out) or else people will begin to arrive for the next Mass.
It would be nice if all the churches contained spaces that would suit everyone; a Mass space arranged how people like, a big comfortable vestibule where people could talk, a separate quiet chapel where people could pray, etc. but most churches, especially those not built in the last 10 years, don’t have all these spaces, and in any event an 80-year-old person with bad legs doesn’t really want to walk around to all those spaces to talk to her friends who she only sees at church because church and doctor visits are her only outing of the week.
It would also be nice if people would have patience with those who do things differently from their own preference. I am not referring to you, Titivillus.