I don't understand this at all. Why would anyone care who has [Bjorn Borg's] trophies? Its not like anyone is going to think that the highest bidder actually won them rather than bought them.
Isn't it? Perhaps not in this specific case, but people in resenting the idea that the trophies might come to be owned by a private buyer are applying a general wish that badges of achievement be held by those that have earned them.
I think that's a reasonable preference. There are lots of ways of displaying wealth, but fewer ways of displaying past exellence at tennis. Turning badges of achievement into symbols of wealth destroys information.
A better example of the same phenomenon is here. I might already know who won the Wimbeldon Mens' Singles in 1980, but anyone on seeing a Blue Peter Badge on someone's lapel might easily assume they'd earned it. If they can be had for a fiver on eBay, that information is lost to us.
There is a complicating factor when such badges become historical artifacts - at that point it is useful for them to end up in the hands of a collector or a museum, where they are linked to their historical context, rather than a descendant of the original winner of the honour. But while the winner is alive, people prefer that the badges stay in their possesion.
To summarise, there is money, and there is honour of achievement. Money can be, to some extent, a sign of honour of achievement, but in general they are different things. People like to be able to honour achievers, and so prefer that those symbols of achievement be usable to determine who is to be honoured.
(Of course, one can still ask why it is that people want to honour achievers, but that's a much wider question).
What to do about this? We can attempt to restrict - by law or contract - the resale of badges of honour by those that earn them, but the enforcement costs are large, as the BBC is no doubt finding.
What does work is to keep the enforcement within the "system of honour" itself, which indeed is what people do. To buy a badge of honour is itself seen as shameful and dishonourable, and, perhaps to a lesser extent, to sell one likewise.
(The same principles underlie in part the loans-for-peerages controversy, but that sort of thing is historically so common that it's difficult to be sincerely upset).