Where a (video-capable, audio-muted) monitor helps with my 1-year-old is that I can see at a glance whether he's just fighting a loosing battle with sleep, or if he has won that battle, is standing up and sleep has lost this battle.
If it's the former, I dare not open the door. If it's the latter, I need to go in and rock him back to sleep. Having this tool has saved him and I from many cranky, nap-deprived days.
And, btw, it's a dumb monitor with a ~400 foot range. All 3 neighbors within range are trusted to watch the kid - if they want to help, great!
We never had any real issues with either of our kids, and only false alarms. But I know my wife got better sleep just because the alarm was there (only in part because I was usually the one to check when the alarm went off).
We stopped using it nearly immediately. It was a glorified audio only monitor for us, the check for movement/breathing was giving lots of false positives and drove us insane.
Other parents even turned on a beep for each breath, made it sound like a hospital. You subconsciously gold your breath if the device beeps with a tiny delay.. beep..beep....???beep
For us it was the wrong choice.
Definitely is a sanity-saver.
Yes, we use a movement-based monitor and have for the last 6 years (3 kids). It doesn't require anything on the baby, and sits under the mattress. Sensitivity is adjustable and it's very accurate. It truly lets me sleep better at night.
Now, what would be really helpful for small babies is consumer-available version of the 'clicker' breathing monitors they use in NICU wards. Our oldest was in NICU for nearly two weeks due to being a little prem, and when we got them home the lack of that regular 'click... click...' from the monitor was so hard to get used to.
It's not a medical grade device like the NICUs have, but it lets you rest easier knowing you'll be notified if your baby's pulse or O2 levels drop.