Hey, so I own a tiny house so maybe I can shed some light on the mindset and address those points you made.
1) Yes, there is some truth to this. For some people this is a trend. They might think of it as hip or cool, and it's on t.v.
For me, it was not a decision based on some stupid trend. It was purely economic. I needed a house close enough to work not to make me hate my life and ruin my car, and I needed to get out of a city where gunshots and drug use were commonplace. A tiny home is usually much cheaper than a "normal" home.
2) Depending on how extreme you take the tiny home thing, I bet you're right: IT could be anti-kid. That depends on the family and the people in it- some people don't seem to need personal space as much as others. Some tiny homes are straight up one room boxes.
People have lived, and can survive in those conditions- but why the hell would you want to? My property has enough space for a couple and one child. Past that, I think it would begin to get to a level I might not be comfortable with. The family who sold the house to me was actually leaving to have a second child.
On the flip side, not everyone actually wants kids. It's also extremely easy to pay off a small cheap property, and then keep it as a rental. You can use this to act as a stepping stone for an actual benefit if you leave.
3) I really think you're off base with this one. Way off. Some people actually have the capacity not to blow their money the second it lands in their bank accounts. I know this seems to be a dying breed in today's culture, but it's true.
As I said previously: I bought a tiny house to save money. I will have my mortgage paid of in a few more years. I will probably be most well-off person I know in my age group once this is done with. If I want to move, I can rent, or just buy another house, or whatever they want to do. That's my business and I'm in my mid twenties so I'd rather not consider that "when I'm old" mess just yet, but I will tell you this: Without the pressure of a mortgage, you can put money into other buckets. Buckets that make you money at a decent rate of return. Roth IRA, 401Ks, HSAs.
I have very little fear of retirement. I also do not understand the fear of renting in old age- there is much less to worry about, maintenance isn't on you, and you can move to a different location if it sucks.