Cruel, having daft host do a tune! (8)

I believe the answer is:

inhumane

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'cruel' is the definition.
(similar in meaning)

'daft host do a tune' is the wordplay.
'daft' becomes 'inane' (I've seen this before).
'host' indicates putting letters inside (inserted letters are hosted or welcomed).
'do a tune' becomes 'hum' (I can't justify this - if you can you should give a lot more credence to this answer).
'inane' placed around 'hum' is 'INHUMANE'.

'having' acts as a link.

Can you help me to learn more?

(Other definitions for inhumane that I've seen before include "Heartless" , "Callous" , "Not compassionate" , "Cruel" .)

I've seen this clue in The Times.

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