An exchange is place where the one without information give plenty of money to the one with information, this is not going to change :).
Other schemes you suggest seem to be based on the corrupt brokers / specialists operating in some US exchanges, and they no longer exist when you've removed the fat dinosaurs (they are disappearing slowly), in real electronic exchanges with no recurrent "upstairs" shadow deals.
Some electronic books are not fully open (hidden sizes, ...) but that's not a real issue.
Then the obvious question (related to your "open" and no one here yet) is why are we setting for continuous time trading from open to close?
In particular I like the way the day closing prices are fixed in some market: everyone has five minutes to put all their buy and sell orders in the book (with no execution), then the price is set to the level that maximise volume and all relevant trades are done at this level. Doing that something like four times a day would be largely enough. If there's a news too close to the five minute, the exchange can delay by 30 minutes or one hour and that's it.
ebay of course could create a formal market for sufficiently similar items :)
but then, no one is forced to do derivatives that price off of the close.
And asianing rules indeed :).
There are many plausible reasons to think 24x7x365 would be bad, for example if you're a person doing your own trading, you can't be awake 24x7x365, so you de facto create intermediate layers of professionals.
To me, as discussed here (assuming you want open capital markets), low frequency (a few times a day or even once every few day, weeks, ...) auctions would encourage people to place long-timed buy and sell orders based on their evaluation of the company traded, rather than short term trends and fluctuations.
Note that in practice traders on currency markets for big banks ("FX" traders) do roll their books from continent to continent each with its own trading team and do nearly 24x5 trading.
Some companies also have their stocks listed on multiple exchanges on different continents (it's called "ADR"), so you kind of have 24x5 trading. Some companies are rolling back those multiple listings (it increase compliance costs and the benefit isn't great any more in the internet age).
