While I agree with a lot of what you say, It will virtually put people in a situation where they might be forced to sit at their computers all day long.
You could make the argument that if you put in your highest bid initially then you wouldn't have to and you would be correct, however in the real world of ebay that doesn't hold true.
As you stated, you sometimes overbid. No one likes to lose an item because the winning bid was just a wee bit more than your top bid. As an afterthought you would probably say, I might have spent that extra buck. It is that factor that would make you sit till the close of every auction.
I would bet that the way things stand now, the vast majority of winning bids are pretty much decided in the last few moments of the auction anyway. How many auctions have you sniped?

Another factor to consider that has yet to be mentioned is what would you do if there were several auctions ending around the same time?
You could go crazy just trying to keep up with all the 15 minute extensions.

One of the main reasons people look at ebay is the hunt for a bargain. If that were to disappear I think many bidders would also.