As a "young" mom in the thick of it I have to say, not as much has changed as you might think. I say "young" because while my age is still young, I feel much older, as I'm expecting our seventh baby next summer and had twins last Christmas! I still have cribs with the sides that lower and I let my babies sleep as they like. Heavens, I would probably get a wrap on the knuckles by the "experts", but my twins have shared their crib together since the first day home from the hospital. They sleep better that way, curled up beside each other. It's so cute, because my little girl twin always scoots over to her twin brother's side of the crib and snuggles up, sometimes even laying on him! And he sleeps right through it!
I also prop their bottles up for their feeds with baby blankets. It's the only way I can do it most days! I breastfed all our other babies, but couldn't keep it up with the twins, especially with them being premature.
I do raise all our kids very simply and let them play by themselves. I had someone over to visit the other day and she was shocked how, once the twins had finished their breakfast of dry cheerios, I took them out of their high chairs and went and put them to play on the living room floor, then came back to the kitchen to start dishes. She was asking if they were okay by themselves and I said, " oh yes they are fine. The two and four year olds will keep an eye on them!"
I will say that one thing that has probably changed is the disposable diapers aren't as horrible nowadays as you described, with the bunching up, leaking and tearing. If you get a good brand, ie Costcos or Sams Clubs, they are pretty good and don't scream plastic. I did do cloth diapers for two of our babies, until the twins came, and honestly with the price of water nowadays, I don't know if it saved much $$$, which was the main reason I did it. I did like the fact that I never ran out of diapers, and if the pile of clean diapers was low, I would just wash another load. But when the twins arrived, they were so small! Even the hospital disposal preemie diapers were too big! And once the twins grew, I was so overwhelmed with two babies plus four other children, washing diapers wasn't on my radar. Costco diapers do the job! Maybe I'll do cloth diapers again for the next baby, since it's just one this time around!
As for little tikes running around in padded footie pajamas don't worry, we still get to enjoy that! I've done the cutting off the feet part of the pjs many times before, too. And then when the pajamas are too old to wear, I cut them into memory bears for the kids. They love that!