came to mention polar, IMO the only "near accurate" HRM is one with a chest strap (not these fitbits or even apple watches). you can get one of the polar watches to go with it or just skip it and do like you said, run the app from your phone. i have a watch because i like to check during stuff like lifting, kickboxing, boot camp and can't keep getting to my phone during that stuff
I had the polar watch (and still do) before smartphones were even a thing.
The watch would be over budget. Fortunately the apps do the same things as the high end watches but like you said you can't just glance at your phone like you can a watch.
It depends on what your doing though, I do fitness boxing, pushups, squats, treadmill....in fact anything and everything I do not use GPS for I use my phone cause I can turn my head or glance at the screen.
If I need GPS like riding or running, I use my polar watch because it has GPS on it. So rather than burn out my phone battery using active GPS and Bluetooth. I just use my watch.
Pretty much any indoor workout I use a device cause there are audible alarms when I enter certain zones. There are audio notifications
When goals are hit and stuff.
Watch or phone/tablet you can't go wrong with polar. Polar first and foremost is a heart rate monitor company, fitbit Apple and everyone else are not. There main focus is not on that type of tech. It's just something they say "oh hey we kind of do this too!"
Think of those like a multitool. It might have a Lil blade on it, a Phillips head, flat head, some other stuff. They are somewhat functional but to get the best of any of those tools you just need the one singular tool designed to get the job done. Polar is that singular company for heart rate monitors and tech.