Yogurt in general is healthful (any yogurt that still contains live cultures, that is). There are many brands, and various kinds, and it can be manufactured and sold or made at home with various ingredients (and often fillers, etc, when manufactured). So it's really important to look on the container of the particular yogurt you're eating to see just what you're getting because it can vary so much.
Even though yogurt is good for gut health, etc, it still contains calories so the total number of calories one might eat could be a factor for "good health." Too many calories of just protein, carbs and calcium may also keep one from eating foods with other nutrients needed by the body, as well as fiber though.
"Greek" style yogurt is just yogurt that's been drained of some or much of it's whey (the liquid part). Whey has more carbs/sugar than the curds or solid part, so if some of that's drained away the resulting yogurt will be lower in carbs than the same amount of undrained yogurt would have been (depending on how much is removed). That's for *plain* Greek style yogurt though... any yogurts which are flavored or sweetened with real sugars will have more carbs added back in. Not many people can eat plain yogurts straight --without sweetening-- (unless cooking savory things with them), so sugars and often fruit too are added to make them "sweeter" which both contain carbs.
The issue of how much fat a yogurt of any kind or brand contains is another thing. It can be made with non-fat milk all the way to full-fat milk, and in the case of some Greek yogurts even some cream.
So again, how many calories are you consuming in a day including the particular yogurt you're eating, and how many carbs does it have or are you adding, and also are you getting all the other nutrients you need to have a healthy diet even while eating a fair amount of yogurt every day?
Re eating dairy, if you're not opposed to dairy in general, that's fine. And if you're not allergic to the proteins in milk, that's fine. And if you're not extremely lactose intolerant, that's fine (since most who are can still consume yogurts because so much of the lactose --milk sugar-- has been eaten up by the bacteria and turned into lactic acid). And if you have no other physical problems from eating dairy, that's also fine (some people feel it increases the mucus in their heads, etc,).