I have been using probiotics for my family for many years now - for food allergies and inflammatory digestive conditions. What I can vouch for is that the probiotics help the immune system for sure - we don't get the flu or colds or such things as often as a "typical" person does - we go out and about every day - in elevators, offices, schools and other public venues. I googled it a long time ago and I found some research that probiotics keep the immune system on alert so that it is ready to fight any new infection.
Another thing that the doctor who originally recommended probiotics told me to do was to rotate the strain of bacteria every 3 months or so. The idea was to get a more broad spectrum of bacteria into the body and also to not let the body get used to the same kind of probiotic bacteria. And this makes sense to me, because many kinds of beneficial bacteria have many different benefits and it is good to introduce many of them. So, I have a few brands of probiotics and I faithfully rotate them every 3 months.
I am not personally concerned about probiotc bacteria becoming useless due to overuse - there are several ancient culures where fermented probiotic foods have been traditionally eaten for centuries and people have remarkable longevity in those parts of the world (foods like miso, kefir, kombucha etc) . Eating these foods have not diminshed the benefits in several generations of people in those regions of the world.
As for gut-autism link - I guess that using a probiotic supplement can not hurt - if nothing else, it can improve the immunity and the digestion of the person taking the supplement. And if you wanted to give it to kids, there are several yummy flavors like raspberry, citrus, chocolate, mint etc. I am sure that it is not a hardship for little kids to take them.