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. If you were to sit in front of your computer and get into a bid battle, at some point one of you WILL reach a limit and walk away. All the while the seller is salivating! If the auction closes as a set time snipe otherwise put in your highest bid and be assured other bidders will 'test' your limit and put you 'all-in' or overbid you.
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. ALL auctions are won by 1 increment; so losing by a small amount is always the case (you just never know what the MAX was).
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. I just had 53 auctions close and 95% of the bidding happened in the last 2 hours How many auctions have you sniped? I snipe most all that I get into, If someone on the board is hawking something I could use I throw in a bid for them. I may get a bargain, or it helps my chipper friend get his auctions started and bid up. AS far as sniping, I set a reminder and will check the auction I am interested in OR I browse eBay looking at things about to close. I don't sit in front of the computer all day.

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. That was exactly my point in making large numbers of my auctions close at the same second, causes a bidding frenzy and people get into competition rather than bargain hunt.

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. most bargains have disappeared already. You hope for a fair price or at least one you can afford on something you don't have. If something caused prices to drop there would be more buyers and the prices would again creep up. The 15-minute rule would help sellers get more. THEN once the buyers realize this would cease to throw in those last minute bids and the price would not jump up thus creating a bargain again, it is a pendulum that will constantly swing as supply and demand change. Do you buy all that??