I started cycling more seriously in 2010 and shortly after that got a polar heartrate strap connected to a watch. It gave me live heartrate, average and maximum for a ride and was a bit of a curiosity. I then got a Garmin with a heartrate strap, which was a bit erratic, prone to dropouts and spikes, but was correlated with height, speed etc to provide me with more data on rides.
Two years ago I got a newer Garmin, with a new chest strap which has cured the dropouts and spikes. I've gradually learned what it does and doesn't do. One thing I have struggled with ever since starting cycling is blowing up on hills. I'm fine with 10-12% or so, but if it ramps up above 14-15% I'm very likely to have to stop. One of the issues with that is if it is a long hill once I have blown it is likely to happen again. Several of the big hills in the North-East of Scotland have defeated me. Oddly they all have an 'easy' side I can do fine and a 'hard' side I struggle with. My real nemesis was the Cairn O' Mount from the Fettercairn side - it had defeated me twice. In the last year or so I have worked out that if I watch my heartrate on the hill and keep it below 155 I can keep going. This year, despite being slightly heavier and not as fit as I've been in the past I climbed the Cairn O' Mount. It wasn't fast, nor pretty, but I made it.
My body is never going to be a finely-honed temple of athletic prowess. I'm too old, work irregular hours, drive too much and am too erratic in the time I spend on the bike. I've a rough idea of my heart-rate zones and do some gym workouts based on heart-rate. I'll do 45 minutes on an exercise bike at a maximum HR of 140 for instance, which sees speed / power tail off slightly towards the end.
So I like gadgets, am happy with the gear I have and have found some real world applications that work for me, but I certainly don't see heart rate monitoring as something I couldn't live without.