The point of Lexus is simple:
In 2010, Lexus outsold Mercedes, BMW, and handily shamed Audi who has always been the runt in America when it comes to German luxury brands. The "luxury appliace" formula that most of Lexus's offerings fall under nets some serious cash for Toyota, and perpetually impressive sales.
Infiniti and Acura have always been lagging in sales comparatively, despite Acura being older and Infiniti being the same age as Lexus. They just didn't have the right formula for selling luxury cars in the States. Acura was "luxury light" from the get-go and still is today, offering smaller engines, smaller cars, and a sportier demeanor. It's a niche, whereas Lexus is the mainstream. Infiniti started out similarly to the Lexus LS400 with the V8-powered Q45 except that instead of being simple and smooth it was full of technology and looked strange in comparison. And look, Infinitis are still crammed with tech and look a bit weird. Despite their niches they both still outsold Audi in 2010. That's one reason the Germans have been steadily coming out with smaller, less expensive cars. The Japanese are pretty darn good at taking advantage of an opportunity.
Lexus was basically a better Lincoln, or a better Cadillac. The other two just weren't the same. Too Japanese for their own good. To this day Lexus is still the "better Cadillac" it was back in the day, and it still outperforms all the other luxury makers.
If you're asking why Toyota, Honda, and Nissan made separate brands, Cale already answered it. Simple as that. Which is strange, because Hyundai is now trying to stick with their name while improving its luxury demeanor. They already have two brands with a bit of overlap, though Kia is a bit sportier. It would almost make sense to turn Kia into a sporty-ish mainstream brand and evolve Hyundai into an actual luxury maker.
