Nobody has to have approvals of private revelations, but they have to have them to promulgate them as My Private Revelation: The Book, or to have anything done formally in church on account of your revelation (“Mary said our parish should hold a procession of sheep every year in honor of Our Lady the Immaculate Ewe-Lamb”.)
If everything is just private stuff, or you’re not affecting many people, it all falls under private piety and you can do pretty much what you want (within reason). Likewise, if you just told the priest, “I’ve got this great idea! Let’s hold a sheep procession in honor of Our Lady the Immaculate Ewe-Lamb,” it would not require any approval process, except your pastor saying he thought that was a good idea too. (It’s actually fairly common for people having visions or seeing apparitions to have prayer suggestions okayed by their priest and implemented, long years before anybody knows about the visions or the bishop approves.)
Of course, Catholic laypeople also are supposed to get approval from their bishops for certain kinds of religious books (like books of new prayers), promulgation of new devotions, etc. If I want to teach religion class in my parish, I’m supposed to take classes from the diocese and get approved. The only people I can legitimately teach without some kind of approval is my own family, and street-level informal evangelism.
Bishops are successors of the apostles, and all the Christian teaching in a diocese flows from them. The early Christians were going to church with their bishop every Sunday (at least), and he knew all about what they were up to.
My bishop doesn’t know me from Adam (well, probably he does know me from Adam, but maybe not from Eve!) My local pastor might know me, but not be enough of a theologian to be able to tell if something is wrong with whatever I’m promulgating. At some point, somebody has to be responsible for saying, “Mintaka is a knowledgeable Catholic who won’t steer you wrong,” or “Mintaka knows nothing/is a creepy criminal who wants to send you to Hell.”