Adrian,
1) It's less formal. I'm there to play golf, not to look at my watch.
2) You meet and play with people that would forever otherwise be strangers if you all found your own little one ball slot for 5 holes after work on a Summers' evening. Think how many clubs run a roll up event and how well that generally works.
3) Tee times are simply not required at more traditional, non-proprietary clubs as the membership levels required to break even are simply not as high. Remember that we don't need to make a profit, you do. Furthermore, taxes and golf on less than ideal soil all add to your burden.
4) Speaking specifically about my club, Hayling, even if a few groups turn up at the tee at the same time, congestion isn't a problem as the natural spacing created by an opening par 3 makes it all work out well. To be frank, they're a pretty well educated bunch that either get round in 3 hours or immediately call quicker players through so slow play just isn't an issue. (Note: The block booking for the small kids on Sunday can be a problem but I'm all for them getting a taste of the game and I'm not likely to start bullying 8 year olds so that I can live with
)
5) Green fee poachers aren't much of a problem at traditional clubs, certainly not like they are at proprieties. Stupid, yes, as you would think a golf thief would at least bother to steal a round from a club with some serious kudos but seemingly those types have a subconscious fear of such places.
6) I rarely get anywhere on time.
7) You simply can't book two tee starts throughout the day. Conversely, I can drive half a mile to the 14th tee and start hitting balls whenever I like. If I'm frequently just playing a few holes after work I don't want to continually see the same part of the golf course so strolling on for a different loop is highly appealing.
Tee times creative a very restrictive concept of playing. Once people have a tee time they tend to think they MUST play strictly from the 1st to the 18th. Cutting from one part of the course to another, even when not affecting anyone, is often seen as one lateral thought too many.
And they're just off the top of my head. If I put my mind to it I'm sure I could think of numerous other reasons.