I guess I'd agree that it's personal anecdote but not that it's untrue. I have run inconsistently for years and just haven't gotten faster. Maybe I've cracked the code now with low-heart-rate training and sprints, but I haven't done it long enough to see the evidence yet. "Just running" did not increase my speed, even if I was consistent, so to me it seemed like my results were not correlated with my training. I could run longer distances just as slowly, and my body composition did not change for the better. Moreover, "just running" did not make me feel good. So for some people (personal anecdata again) it is fair to say that running gains may be slow and seem uncorrelated with training.
I did make very very quick gains by "just lifting" and so felt very differently about it. These gains were both in strength and body composition, and within only a few months I found that I could impress people. Not at all like running: it's years and I still can't run an 8-minute mile.
If you're running inconsistently, then it's no surprise why then.
I've lifted and run at various times in my life, and I found running a lot more rewarding, especially with all of the bad advice out there that surrounds lifting.
After the past 5 years of mostly running (with some time away at times due to injuries), I went from a 12 minute mile to a sub-7 minute mile in 3 years (with 1 year not doing much in the way of exercise). Consistency with the frequency of exercise matters a lot.
> I went from a 12 minute mile to a sub-7 minute mile in 3 years
A 5 minute difference. Which is amazing. But only to other runners.
Going from a 50kg (110lbs) squat to a 130kg squat (286lbs) in 3 years is almost trivially doable (I've once gone from 50kg to 100kg in 3 months) and is impressive to everyone.
As much as we'd like our motivations to be pure, we really really really like impressing our friends.
This is absolutely untrue, and purely personal anecdotes. Otherwise agree with your first two paragraphs.