for another five minutes after a bid is made. That seems to be a
perfect solution to me...
That sounds like a good solution to prevent sniping but is not necessary to
ensure fair auctions.

There would be nothing unfair about it - simply another set of rules.

but a few seconds, but everyone gets a chance to raise their bid, until
nobody wants to go over the standing bid.
eBay does that by bidding for you up to your maximum.

eBay won't change your mind for you - that's the difference. Real
auction is a game of emotions.

bid until it is too late to counter. The only reason this is successful is
because, given time to respond, people give in to competition and raise
their bid.

Precisely, and as long as the current system is used, I will take
advantage of it.

Bartek