Is it a good idea to buy CD players over 10 years old even it is a reliable brand?

No.

Definitely not.

Why buy a used CD player when you can buy feature festooned reliable latest technology from companies like Marantz, Sony and Arcam for an awful lot less than $2-3k?

Certainly not for sound quality either. CD players from the 80s can match recent designs, depending upon taste, but unless there’s some quaint anachronistic reason, why ever go there?

The only CD players I ever heard that stood out sonically (albeit marginally) were the Linn CD12 (scale), Rega Saturn (analogue) and the Cambridge CD4SE (vivid tones).

None of them are cheap enough or easy to get hold of to warrant my swapping them for my Marantz CD6000ki - which I think sounds more tonally balanced than any of them.

I'm not sure I even belong on this blog. I bought a used NAD CD player, built in 1999, for the princely sum of $50. The display is shot, even after replacing the backlight. But it still spins discs and has a digital output that I utilize through a fairly recent Arcam DAC. The playback, trough it's resident DAC via the analog out, is also listenable. I assume this deck will crap out, at some point, never to be repaired but replaced with a similar machine at a similar price. 

I would not buy a 10 year old player, even if its moving parts are still available as of today you have no guarantee that they will still be available a couple of years from now. 

From how the question is phrased, I'm sure that Faust understands that disc spinners can break down, so I'm definitely in the camp of being reluctant to buy these -- for one thing, you just simply don't know how many hours are on it. I had a wonderful Proceed PDT3 that just conked out a year ago after 18 years of use and I had used it heavily! And it was the transport mechanism and could not be serviced. So as others opined, for more expensive disc spinners make SURE that they can be serviced.  
  I replaced my transport with a media server.

Comment #2: I don't think you can assume that players today are better than those of 20 years ago at a roughly similar price point. Companies like Madrigal, Mark Levinson, were driven to produce fantastic players in the new field. Today? I'm not sure they are and I've heard mass market players, such as a Marantz I recently auditioned ($400), that had all that digital hash jitter that we thought should have vanished by now....