This is wrong.

It's a shame how the church has relegated most contemplative practices; the only ones who do them are either monks, nuns, or lay saints.

This is simply not true. Contemplative prayer is considered a universal vocation in Catholicism. Reginald Garrigou-Lagrange was very insistent on this point, and nobody would mistake him for being liberal or modern. On top of that, if you're not a cleric or monastic, you're supposed to be a "lay saint", so I don't see what the point is.

Have you heard about the Desert Fathers? They were a bunch of christians who, tired of how popular christianity had become in Rome, and how it had become a religion and not a practice, retreated to the desert, to conduct their spiritual life and practices.

No, they were a bunch of Christians, who absolutely did recognize the authority of the Pope (scroll down to Alexandria, it's mostly Desert Fathers being quoted), who retreated to the desert in imitation of Christ in the desert. Furthermore, I don't even know what "it had become a religion" is even supposed to mean. It really just sounds like a buzzword.

Have you heard of Teresa of Avila's The Interior Castle? She basically described, in her language and from her understanding, the stages of absorption one can achieve through meditation. They're comparable to the samatha jhanas (states of absorption through mindfulness of the breath). She's missing one or two, if I remember correctly.

I haven't read The Interior Castle but I'm vaguely familiar with how it goes, and while I'm not familiar with the samatha jhanas, I'm pretty sure they don't end in spiritual marriage with God. That's the elephant in the room when discussing the similarities between Catholic and Buddhist mysticism, Catholicism is personal and ends with God, Buddhism is impersonal and ends with permanent death. Either way, you don't ascend Mount Carmel by breathing.

To get to my point, Catholicism does have a contemplative/meditative tradition, and you might want to look into that as well. Search for Ignatian parishes, or maybe Franciscan. I'm not too up-to-date on the exact groups that still practice contemplation.

All religious orders exist for contemplation, this is their primary purpose. The question is whether they engage in apostolic works, like Dominicans, Franciscans, and Jesuits do, or if they do not, as Benedictines commonly are. The slogan of the Dominicans is "to contemplate and to share with others what is contemplated", Franciscans have hermits and convents and St. Francis himself thought of the earth as his cloister, and Jesuits begin with their meditative practices developed by St. Ignatius.

From a philosophical perspective, going back to pre-Christian Greek thought, it's a debate between whether or not contemplation is an end of itself. This idea won out in Eastern Christianity but is not in favor in Western Christianity, with the ideal being considered to be a balance between action and contemplation. There are legitimate arguments for both positions.

The reason I mention looking into your own church's "obscure" practices is seemingly subjective: it's possible that once you've started to meditate intensely, you'll see through most of what the church wants you to believe. I'm not saying that their beliefs are silly, or false. I'm saying that their focus, their ways, aren't exactly great.

This is another ridiculous statement from the perspective of Catholic mysticism. No genuinely Catholic mystic was out of step with the Church, even St. Catherine of Siena, who told off the Pope, did it because of her fidelity to the Church, not in spite of it. The idea that mystics operate in some inherently heterodox plane is silly. Even controversial figures like Meister Eckhart or Thomas Merton never, ever renounced Catholicism or professed heresy.