Nasty people won’t ultimately think highly of show (11)

I believe the answer is:

demonstrate

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'show' is the definition.
(I know that show can be written as demonstrate)

'nasty people won't ultimately think highly of' is the wordplay.
'nasty people' becomes 'demons' (I can't justify this - if you can you should believe this answer much more).
'ultimately' suggests the final letters.
'think highly of' becomes 'rate' (I've seen this before).
The final letter of 'wont' is 't'.
'demons'+'t'+'rate'='DEMONSTRATE'

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(Other definitions for demonstrate that I've seen before include "Prove, show" , "Show or display" , "Prove - protest" , "English floozies returning, led by villainous character" , "Review" .)

I've seen this clue in The Times.

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