This was my approach as well until I noticed my Garmin HR zones were all out of whack. I would go out for an easy jog and Garmin would say I spent the entire time in zone 5 because the HR zones are set by 220-age. As a person who runs 2000+ miles a year, 220-age simply doesn't cut it. This is what sent me into the health app looking for my resting HR and I found out I couldn't find it. I then found a third party app that would export health data to a csv file and I thought I was good to go. What I got was a bit of a mess. When I export from Garmin to a csv file, I get data that is already in a format that is useful to me as a runner. I get HR, cadence, distance, etc and they ar all in units that I expect or that require little or no conversion to be useful to me. I just took a look and I have 366 runs recorded, each of which is downloadable as a csv. I also can download summary csv files of 20 runs each. I haven't done this but I plan to do it so everything is "backed up" locally as a csv file should something happen to Garmin or I decide to move on to a different provider. Interestingly enough this is part of what brought me to Apple in the first place. I own my data. I can bring it in when I want, I can download and back it up when I want and I can take it and leave when I want. Apple has been making it increasingly hard for me to exercise what I consider to be "normal" control over my own data and the health app is a huge offender right now.
Yesterday I ran 10.5 miles including some intervals in the mid seven minutes per mile. Later in the evening I looked at my RHR (Resting Heart Rate) and I was happy it had drifted down to a number that I can now use to adjust Garmin's default (clueless) HR zone settings using what is called the HRR (Heart Rate Reserve) method.
If I wasn't trying to monitor resting HR, or if Apple would at least make it easily available I would be happy to wear my Garmin only for running. I also like the idea that if I want to do a run, my Garmin is always with me. If AW and iPhone apps hadn't proved (for my usage pattern) to be quite so useless, again I wouldn't mind being without my Garmin for a run but alas I really feel it's worth doing without the nice-to-have features to have Garmin's must-have running features always with me.
I ran "two-wristed" a few times when I wanted to compare iPhone running app performance with Garmin performance. The result was "no contest" so I stopped going two-wristed almost a year ago. I went "alternate wristed" (only wearing AW on days I didn't run) until I got a Garmin 235 that includes the ability to get notifications pushed from the phone over bluetooth. Garmin's implementation of notifications was almost as good as AW so I didn't miss not having it. Later I noticed I was getting as frustrated with phone calls texts and other reminders during runs as I had been with AW so I wound up disabling "smart notifications" on my Garmin. This was the last nail in the coffin of AW. I was so turned off by interruptions during exercise, I was willing to simply do without wrist-based notifications all the time. It probably doesn't help that Garmin's user interface for turning notifications on and off is rather clunky so I'd rather leave it off than hunt for the setting before and after every run.
If I don't sell my AW before the end of marathon season, I might go back to wearing it some of the time but for now there is a pretty high likelihood I'll get rid of it before then.