Bill, using an arranger doesn't necessarily mean it sounds just like the record. TBH, I am not honestly impressed with what arrangers do to EVER feel they sound 'just like the record'! And club owners over here hire musicians on exactly the same criteria they do in the UK (I know, having played both)... whether the entertainer 'entertains' the crowd.
No offense, but if an arranger player would get replaced by a CD, he's not much of an entertainer! The singing (instrumentalists are almost unknown over here apart from cocktail piano - I don't know of a single act in my area that is instrumental arranger) and audience interaction is what sets them apart from a CD. You might just as easily say that, if a club owner is willing to replace an arranger player with a CD, he could (for exactly the same reasoning) replace his solo guitarist/singers, or his jazz trios, or full rock bands. It would save him the same money.
I am curious. From your post, it would seem to imply that anyone that uses an arranger gets fired in Britain, for sounding fuller than a solo piano or organist. I find that hard to believe!
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An arranger is just a tool. What matters is what you build with it..!