In my experience, it worked the same way as sharing a room in University. Yes, your side of the room certainly has a "you" quality to it, but even with partitions and clever arrangements of closets and shelves, it's not the same.
When you have your own space, you're completely free to roam. You no longer need consent/approval from anyone else and you're free to customize things as much as you want. When you share a space with someone, you always partially depend on them in some capacity. When you're only sharing with people in your own company it's much easier to deal.
Also, in a co-working space, you could be sharing the conference call set-ups, the conference rooms, you have to arrange splitting the electricity/water bills, etc. All in all, it just results in more headaches.
Private offices can solve the headache of a bad co-tenant, but have their own headaches as well. The obvious one is that it's more expensive. A less obvious one is that you loose the access to outside people. If you're working near someone else, it's fairly trivial to go ask them what they think about something. You're likely to talk to them anyway, so it's an easy way to get an outside perspective by someone probably in the same industry. It's a natural form of networking as well. There are certainly benefits to having a private office, but it's not nearly as cut-and-dry as you're implying.
This advice doesn't help most startups, who haven't raised big funding.