Keeping it quiet might be a thing given the moral outrage this would trigger.
The main obstacles here are access to donor eggs and surrogate mothers willing to carry. This may already have happened. Additionally, failure rates acceptable with dogs and livestock are going to cause moral outrage. Though if you look at IVF, the success rates there are not great and it is considered acceptable anyway. Never mind the discarded embryos, miscarriages, etc. Many couples try for years before succeeding.
Ongoing progress might make a few of these things easier. E.g. producing egg cells from normal cells might become feasible. Also there is some progress with artificial wombs. Add to that improvements to gene manipulation and you are looking at industrial scale production of clones of all sorts of species. I see this more as a question of when than if. Human cloning is inevitable.
The main obstacles for this are entirely non technical. There are enough religious and political constraints that this will have to happen under the radar and in less strict countries for a while. Barbara Streisand cloning her dogs sort of moves us toward that though.
Puppies are cute and so what if they were cloned? Are human babies so different? You can bet that there are some dictators, billionairs, etc. out there that would love to have a "mini me". It's the ultimate in narcissism and hedonism. Trump might be interested, just saying ;-). He's insensitive enough to not give a F* what everybody else things. This baby is going to be great. I will be the best child ever!