I guess it depends on the rental vs purchase market where you are.
Here in outer London, rental prices are pretty much in line with the interest payments on a mortgage. So you're "throwing away" the same amount whether you're renting or not. I'd have thought this would become a natural equilibrium in most places. If rental prices are significantly more than the interest payments on a mortgage then owning will seem more attractive.
Mortgage still has value in that it gives you the opportunity to invest that in a house if that's something you want to do.
Early in a mortgage you're paying what, 25% principal? Probably less? And that's not even taking into consideration property taxes, mortgage insurance, etc, etc. So no, you're not getting $1k back from every month.
You wouldn't get $1k a month in equity. First of all, you can't ignore interest as its a huge part of what you pay on a mortgage. Depending on your down payment and rates, you could end up being over half the cost of the actual property in interest and property tax. Then there's maintenance, insurance (much more costly than renter's insurance), and so on.