I came from running, went to cycling, now do a mix of both.
Not sure how running is especially more convenient or time efficient than cycling. It doesn't take that much longer to put on a helmet and clip in.
That aside having done both, I do continue to ride. I will say that nothing I've done in cycling quiet beats the feeling of being in sync on a great threshold run or even one of those good days when your whole body feel efficient and grateful, as if you're almost skimming the ground in flight.
Cycling wins for me in some other ways:
1) Diversity is one. Running is pretty much the same thing, one foot in front of the other and repeat. Cycling has climbs, it has sweeping downhills at 50mph, technical switchbacks, etc. It has group rides that are dynamic in a way that a race, let alone a run, never will be.
2) Racing - Racing bikes beats racing on the roads. This goes out the window a little if your incredibly high level, but unless you're at the absolute top of your competition every running race is a time trial. Run as hard as you can from A to B. Which is great, and one of my favorite ways to race. But on the bike races are much different, and much more tactical. You can try to draw out people for a breakaway in a 5 hour race right from the start, you can attack up a climb and try to solo away, you can try to keep the group together and then win in a field sprint.
It's also sorta nice that different body types can do different races. In running, unless your a sub 20 BMI type guy you're not winning or even being competitive in many races, certainly not beyond the mile distance which is...nearly every road races. On the bike, depending on the terrain anyone can be competitive. Wanna put on 30lbs of muscle and have some sprint power? You can do that and be a deadly crit and flatter road races. You'll never win a hill climb or road race over tough terrain but you don't have to race those. Everyone can carve out a niche for themselves. Some really good races are even set up in ways that every type of rider has a chance of winning with the right moves and right conditions.
3) I don't quite know how to title this, but because of the physical damage you can't really just hammer here or there on runs. In cycling it's perfectly reasonably if you're feeling good to just rip it up that local 6% mile climb for 3-4 minutes. Same thing with group rides, you can get really competitive on a group ride or something without it torpedoing your training. It's part of the reason strava, while good for runners, is probably 10x more interesting for cyclists.
4) Climbs - This one is more personal, but damn does it feel good to fly up a hill on a bike and get into the rhythm of climbing. That comes close to approaching the same good feel I get from running. As someone that always sucked at running anything vertical, being strong at that on the bike makes both the ups and downs awesome.
So with all that said, I generally prefer racing bikes over racing on the roads, but certainly still enjoy hopping in the occasional road race and really pushing it with all I have.
I will admit though, if every run felt as good as that 10% of truly good runs do, or maybe if I ran uphill well...I'd probably never touch my bike again.