Even better, if you're going to go to that extreme to restructure your life, is to simply attack the problem directly. If you're concerned about your possessions owning you, just fix that. Watch a few episodes of "Clean Sweep" to get in the mindset, then clean your place out, and make sure you do this periodically.
Ownership has benefits too. In my opinion when you rent everything you are simply trading a situation in which your possessions metaphorically own you for a situation in which your possessions more literally own you, or rather, the person who actually owns them owns you. Everything you rent has a contract attached to it; what's the fun in that? My house is full of things repurposed; an entertainment center with the top cut off, chairs with customizations induced by pets, a couple of doors I've added internal cat doors to. Chunks of the "house" I've sold, chunks I've added. And I'm not even "handy".
Excellent point; once you're good at "ruining" or getting rid of stuff, the stuff you have doesn't bother you. The more you get rid of, the easier it gets, because you realize you don't regret any of it. Once you've got over the horror of throwing away valuable things yourself, you can exploit it in other people. "Hey, do you want...? If you don't, I'm just going to throw it away." Your stuff ends up in their closet instead of yours. You can also donate stuff to friends who enjoy having garage sales or selling at flea markets.
Bottom line, as with alcohol, there's no need to avoid it unless you know you can't handle it.
It sounds like both approaches are ways of dealing with the same root problem: attachment and the illusion of control.
IMHO, renting vs owning isn't the real issue. They're both just different ways of financing. The issue is the overdeveloped attachment people get to the "stuff" in their lives.
List exact list of things you need, clothing articles, personal hygene... all minimal, and keep what is minimal. If you want something find , something you can or want to get rid of. This will keep balanced list of items in your life - without weight dragging you down.
Best possible response. When you rent you are constantly and painfully aware that this stuff (whatever it is) is owned by someone other than yourself and that you are paying them for the 'privilege' to use it.
Ownership has benefits too. In my opinion when you rent everything you are simply trading a situation in which your possessions metaphorically own you for a situation in which your possessions more literally own you, or rather, the person who actually owns them owns you. Everything you rent has a contract attached to it; what's the fun in that? My house is full of things repurposed; an entertainment center with the top cut off, chairs with customizations induced by pets, a couple of doors I've added internal cat doors to. Chunks of the "house" I've sold, chunks I've added. And I'm not even "handy".
Don't treat the symptoms, treat the problem!