In my experience (4 dc, 1 diagnosed Sen) it very much depended on the child.
Dd1 got weeing around 2. She just didn't equate the sensation of poo with the mess that then occurred for another few months. She had ds1 arrive just before her second birthday and yes, I will admit with dealing with a newborn, enforced potty training at 2 very definitely went out of the window. We tried again over the summer she turned 2 and had reasonable successes. by the age of 3 she was dry and clean day and night.
Ds1 on the other hand point blank refused to potty train until he was 3.5. I was at the stage of believing he would be in nappies when he started school when all of a sudden he decided he wanted to be a 'big boy'. He also had to contend with twin siblings arriving just before his second birthday and again, forcing the issue just wasn't on the agenda. It wasn't like I wanted to be changing 3 poopy bottoms but ds1 did everything he could to avoid using a potty or toilet. He would even wet and soil himself deliberately! (Even at 8 he will occasionally wet himself mid-meltdown)
Ds2 was an absolute breeze and was dry day and night a few weeks after his 2nd birthday. Which made it even more frustrating that his twin sister just wasn't interested. She would happily play in wet or soiled clothes if left (and nursery did, accidentally, one day). It was nursery who asked for her to go back into nappies as they didn't think she was ready. She was daytime dry and clean just before her third birthday. Nearly a year later than her twin.
Dd2 is now a couple of months off 7 and despite following advice re liquids and timings etc from the continence clinic, she still isn't reliably dry at night. There are believed to be some Sen issues at play.
Yes, I do believe there are a large number of lazy parents. And the increase in use of pull-ups likely doesn't help. But I think the nappy companies need to take responsibility for this as well, advertising pull on nappies for babies as soon as they can crawl away! They are allowing people to take the easy option out from a much earlier age.
Perhaps the waste collections could encourage earlier training by charging for disposable nappies to be collected? (There are companies who already do this so nappies don't go to landfill but are incinerated towards energy production instead).
Maybe the real nappy movement needs a rocket up its arse in our disposable society. I used reusables with dd1 and ds1 but couldn't keep up when I had 3 in nappies.
Maybe nurseries need to work with parents instead of imposing their own training schedule - a friend put her daughter in the same preschool mine had been at, and due to a change of management they insisted on potty training from 2. The little girl was kind of ready but not quite. They had rigid toilet breaks and complained when the child a) didn't go and b)was then wet 10 minutes later. They initially refused to move the toilet break but a complaint went in. Suddenly toilet breaks became a free flow movement and there were a lot less accidents overall in the preschool.