We did the alarm and found it horrible and pointless. It goes off only when the kid is already wet, so what's the point? We still had wet pajamas, wet underwear and wet sheets. Our pediatrician recommended that we see a pediatric urologist, even though medical issues had been ruled out, which we did. He was great. He assured us that nocturnal enuresis ("nighttime bedwetting") is extremely common, particularly in boys, and that he had patients far older than our son who had the same problem. He said it's totally developmental, like when their molars come in and when they get their growth spurts. There's nothing to "train" a kid to do.
After discussion, and after we shared this was interfering with our son's social life (no sleepovers, no camp), we chose to use a medication called DDAVP. I'm not big on meds for no reason, but the side effects were virtually nil, and it was one pill per night at bedtime. It took about a week or so to kick in (I think - it was a while ago), but then he never had another wet night. He stayed on the medication from age 7 to age 11 or so, and then he decided to go off. After about a month or so, the problem came back, so he went right back on until he was 13. Then he went off again and his body had developed enough for his brain to get the "full bladder, wake up" signal.
The urologist told us he had patients up to age 18 using it sometimes. He also felt it was far more important that our child get a good night's sleep for brain development than to spend years waking up wet or being awakened by us to go pee at 1 AM.
It was very easy to send our child with 1 pill in a blank pill bottle to sleepovers, and we just gave the parents a heads up that he needed to take it before bed. Some parents knew what it was for, and others didn't. If questioned, he just told his friends he had allergies. Easy as pie. When he went to sleep away camp, the nurses handled it - and there were so many kids on different meds, it attracted no attention whatsoever.
I'd get a second opinion - my son is 27 now, and I'm shocked that your pediatrician, nearly 20 years later, is acting like your son can control this.