For those of us who know at least some Latin, it’s a chance to see how Latin was used by the Church for centuries.
For those of us who had Catholic parents, grandparents etc., it’s a chance to experience worship as our ancestors worshipped. This to me is not “hip and trendy nostalgia”, it’s an actual connection to my now-deceased forebears.
Latin Masses are also often (though not always) celebrated in old, very ornate churches that somehow survived all the modifications of post-Vatican II, so you get to see the large, high altar actually in use.
The services are more geared towards ritual, history, and well, worship, than with trying to connect with modern people or with trying to encourage people to “build a relationship with God”. It is a different emphasis. Frankly, in some ways I would call it “advanced Catholicism” because you need a depth of knowledge and interest to appreciate what’s going on during the ritual, especially with it being in Latin. It’s not the type of thing where someone could just walk in off the street and have a clue. There is definitely a feeling of being among one’s “tribe” of devout Catholics when you go to a TLM Mass; the Christmas-and-Easter Catholic set are probably not going to attend.