I eat yogurt or kefir after taking antibiotics and when recovering from a stomach bug. I think it helps. I won’t be all broken up if someone proves it’s just a placebo, though.
Um, seeing that probiotic supplement hype is heavily tied to their supposedly re-establishing “healthy” gut flora, a lack of evidence for significant alteration of that flora does indeed cast considerable doubt on said hype. 
It certainly helps me sleep better at night knowing that.
Look, each gut microbiome is a complex ecosystem. Start with that fact.
Imagine another complex ecosystem, a large lake. Imagine that something has happened to the ecosystem that several species of fish that are usually predominant there have too little food to thrive and the populations have collapsed. Other fish mostly occupy the niches that exist. Would throwing some extra numbers of those traditional species of fish into the lake make a lasting change in and of itself? Of course not.
First you need to make sure the ecosystem would support them, then maybe an initial stocking can take and become self-sustaining. If anything recreating an ecosystem that supports the traditional fish species is more important to building up the populations than stocking would be.
Tossing probiotics in is like that.
Total number of bacteria in the human gut is estimated to be something like 3.9 10[sup]13[/sup]. A typical probiotic supplement has maybe 2010[sup]9[/sup] bacteria, if it has as advertised, and same for a serving of kefir and likely yogurt.
If the basic structure of the ecosystem, the foodstock, etc., that is not supporting the traditional biodiversity, is unchanged, why would throwing in a fraction of 0.001 percent of the extant bacteria population work to displace those other species from their established occupation of the niches? They displaced them for a reason.
It is of note that the study cited by Jackmannii explicitly excluded any studies that did anything other than introduce the probiotics. Changing the diet, so on, anything that changes the basics of the ecosystem not allowed.
You want a more traditionally biodiverse gut microbiome? Eat lots of real foods that are high in fibers (yes fibers, real foods contain a variety of different ones) and starches that are resistant to digestion. In that context maybe some probiotics too would marginally help.
Otherwise the role of probiotics is helping reduce the impacts of specific transient disturbances, such as reducing the incidence of antibiotic associated diarrhea, and the as stated, of doubtful impact otherwise.
The lack of food is distinctly unhealthy. An excess of food is, in proportion to the excess, similarly unhealthy.
Anywhere between that and you’re probably alright.
Which is to say: It’s food. Eating food is, yes, good for you.
When I had a terrible GI infection in 2005 and was recovering the GI doctor recommended yogurt. I said I hated yogurt, it made me gag (sorry, yogurt lovers, but to me it smells like milk/whey gone bad). He said try it again, given my starved state (I had lost 30 pounds in a month, one week of which I’d been unable to eat at all) it might appeal to me more. Well, yeah, sort of, I got about 1.5 spoonfuls down before my gut attempted to send it back.
After which the doctor said try probiotics and recommended some specific ones. Not sure how much effect they really had but the doc said that in my case my natural gut flora had been devastated and while it wasn’t a definite thing he felt the science was strong enough to recommend them to help rebuild a normal gut environment.
Is yogurt healthy? Yes, to the extent any dairy product might be - full fat versions may not be a good idea for some, and adding sugar is of questionable value at best - but it’s not essential to good health as everything yogurt has you can get from other foods as well.