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I think my single favorite is the Norwegian Chamber Orchestra, because how many orchestras do this?
Other favorites include...
The London Firebird Orchestra:
The New Century Chamber Orchestra:
But there are many more outstanding chamber orchestras out there. Look into the Orpheus Chamber Orchestra, the Chamber Orchestra of Europe, the Concertgebouw Chamber Orchestra, the Mito Chamber Orchestra, the New York Classical Players... and I'm probably still missing several that I love.
It's fairly common for community orchestras and college orchestras to bring in members of the nearest professional orchestra as concerto soloists. Especially when you include college orchestras, that's a lot of solo opportunities to go around. In just the 9 years I've lived in Sacramento, I think I've seen 80-90% of the violinists in the Sacramento Philharmonic, and a good number of the other musicians, listed as concerto soloists with other orchestras. Some of them more than once. (I haven't necessarily attended the concerts, just seen them advertised or listed on orchestra websites.)
So it's not as if musicians in professional orchestras can't memorize. It's just that most of them are only willing to memorize when they are traditionally expected to, i.e. when they are the soloist.