Like a lot of things, it isn't a simple answer.  In my opinion, it depends a great deal on the specific situation and the skill set of the rider.  

Agree with @anchskier : bike handling skills are a big part of this, but so is situational awareness.  Are you in a car-free area, with known terrain - or are you mountain biking down a rocky/rutted/twisty trail at high speed? 

Safety first (for yourself and all others nearby). I take photos on nearly every ride I'm on, never had any crashes or close calls - never endangered anybody else, as I check and re-check myself and surroundings first, and make sure that I am not putting myself or others in danger.

I love this topic! I used to be a freelance photographer before working at Strava, photography is a huge part of my life. As an avid cyclist now, I often take photos while I'm out riding. I love being able to capture the scenery, the ever changing light and shadows, and of course, capture the best angles of all the pastries I consume! I used to bring my chunky DSLR camera with me on special rides, but it was uncomfortable and heavy -- overall highly impractical. I've seen cyclists with special harnesses/straps for bigger cameras, but that still looks like a hassle to me.

I purchased a more compact camera (Canon PowerShot G7 X Mark II) that fits in my jersey pocket and this has greatly improved the experience. Somedays I just use my iPhone and that does a fairly decent job. I must admit that there have been a few precarious occasions -- not being able to tuck the camera away in time, compromised bike handling, camera dangling from the handlebars, etc. Those occasions have been good lessons and I will more often than not sacrifice a photo opportunity if the risk is too great.

It really comes down to how well you can assess risk and apply logic and discretion to situations, and your ability to be prudent, which may vary greatly from person to person.
Here are some of my favorite shots from my adventures: 

Great photos - once did a MTB through the Saguaro National Park west of Tucson - amazing scenery.

Photo's look great! Would you use a mounted sports camera instead or are they not really good enough yet?

In short , NO, on a safe stretch of road/trail to pull phone from jersey or bar feed bag... double click side button to open camera.... look to make sure thumb is over shutter button... then point to view/trail/bird/animal/etc... start clicking thumb (usually without looking).   Press power/lock button and put back in pocket.

Riding one handed is easy, same for getting bottle out of cage and drinking or opening a bar to eat while biking.... same procedure/risks.  Obviously in the city, singletrack or gnarly gravel it can be tricky (similar to fueling or drinking)...but you can pick your moments that make sense.  Also easy enough to quick put hand back on bar partially while holding phone (or waterbottle/bar/gel).   If I want to compose a good quality shot, then I am going to be stopping usually.

Sounds wonderful. I've only been to the eastern Saguaro NP, which was a ridiculously fun but short one way route, much akin to a rollercoaster for bikes. I had never really seen such grandiose cacti before going there, I would love to spend more time in Tucson!

Thank you. A friend just gifted me a GoPro he never uses, so I'll be trying that out soon on my K-edge handlebar mount -- for videos, not photos though. I'm not a fan of the distortion. I haven't looked into other sports cameras. What do you think of the available options and have you tried any?

Great discussion.  I do not take pictures while riding my bike, because for me it could be dangerous.  For the first couple years after I got into cycling I had to hydrate through a camel back pack because I wasn't steady enough to take one hand off the handlebars to grab a water bottle.  I'm more co-ordinated now, and will use my left hand to grab the bottle for a quick drink.  I wouldn't trust my skills enough to take pictures though; I still pull over and stop to do that.

@VikK - The mounted sports cameras are great, but they have their limitations.  I currently have a GoPro Hero 10 that I am getting used to using.  The video quality is amazing.  I still can't figure out how the stabilization is so good when mountain biking.  I can have it fixed to my handlebar, yet I can see in the video where the cables and bars come into and out of view by a significant distance despite knowing the camera is moving just as much as they are.  The main drawback to it is that it is fixed to one spot with one perspective.  I can take photos with it and/or take screen captures from it's feed, but it is only looking one direction and from one elevation.  When out biking, I often want to get photos of things off to the side or from a perspective above the trailside brush line.  This is where the phone comes in.  Many times, I can pull it out of my jersey pocket, take a photo, and put it back without ever even looking at the phone more than a general glance to make sure I am pointing in the right direction.  I usually take a number of photos as I move the phone around so I can pick the best one when I have a chance to review them.  

I haven't tried any so was curious if someone who takes pictures think they are any good. I have the same balance skills as @Jane11 , I still won't grab a water bottle on the move! 

@anchskier and @CreakyCrank  thanks for the input! On my rides, I'm always finding spots to take photos and make a snap decision to stop and take a photo or risk trying to take one one handed.  Have you ever tried bike mounted or helmet-mounted cameras for taking photos for strava? 

@Soren  I've recently been trying out a Gopro vs an iphone. My main issues I have with the gopro are:

1) if it is helmet mounted it adds significant weight and throws my head off balance - also looks questionable! 

2) the process of reviewing photos/videos from the gopro and getting them uploaded to strava is long and cumbersome. 

I agree on the fish eye distortion - doesn't look natural. I've tried the "flat" setting on the gopro and find that is fairly good. 

@Jane11 I agree! I'd love to take more photos and add to my strava posts, but find it a challenge to do so while on a ride.

@Jane11 @Soren @NickRunBikeMN and others, any input on this type of helmet camera product? https://www.kickstarter.com/projects/rh-1/rh-1-performance-cycling-helmet-with-integrated-video-camera/description 

It looks like a great solution, but unfortunately the company wasn't able to complete their product development. 

Totally agree! I see a lot of posts from people taking selfies while riding and it seems too risky.  It would be great to be able to do selfies or landscape shots without having to stop or put your self at risk.

@Soren beautiful photos.  Any comment on the process from getting your photos from the canon photo, onto your phone, then into strava?

Thanks for sharing, I hadn't seen this proposal, too bad they didn't get into production for it. There's a lot of cool stuff packed into this, including MIPS. 3hrs of continuous video streaming / recording per charge seems pretty good too! I also like that you can control the camera system through voice control.
I think I prefer the perspective from a helmet mounted camera vs. a chest mounted one, but I do think that it would affect my ability to look around as freely if it were mounted on my head, but I'd have to try it out to know for sure.
Have you seen SAFA Brian's cycling videos? He uses a variety of cameras, including 360 and chest mounted ones and his footage is absolutely phenomenal. I know he's quite a controversial figure in the cycling world but I thought it was worth mentioning since he does POV videos like no one else.

thank you, Dan! It's super easy and mainly why I got that camera before going on a bikepacking trip last year. I use the Canon Camera Connect app on my phone to download the photos via wifi, do a quick edit and then upload them to my Strava activity.