Adding live organisms to complex living systems tends to have unpredictable and destabilizing consequences. Invasive species being introduced to ecosystems can have knock-on effects that go far beyond their immediate biome. The human body is a complex living system, and the consequences of perturbing that system are difficult to predict.
There are probably also lots of "good" bacteria in the mouth and gut using salivary lactate. I could not begin to guess at the number of additional metabolic pathways happening that are related to this. Not to mention the mutacin production that they mention, that they think may also kill off some of the bacteria in the mouth, that hopefully isn't replaced with nasty S. aureus, C. difficile, Candida.
The gut flora angle is just a whole other rabbit hole.
In light of the potential benefits, the "reasons not to" might fall by the wayside, hopefully none of the cautions end up being a big deal. But the status quo doesn't suck that much, if you look at how bad it could be.
Personally, I would like to see more resources go to diagnosis, study and understanding, rather than seeing people try to jump straight to the silver bullet and test on volunteers. Is it moral because they are "volunteers"? Are they really volunteers given that they would most likely get paid?
More importantly - and I cannot emphasize this enough: If this was such a great and simple solution, evolution would have already given this mechanism to us to and other animals. There is (or was at some point) a very, very good reason that our bodies don't already do this.