>> How about using the same delay blink-matching-delay that is used
>> after showing a matching paren, but in this case to show
>> a character at the other end of the pair with a delay
>> before deleting it?
>
> Makes sense to me, but I'm not a regular user of delete-pair, so I don't
> know whether that'd be annoying or reassuring...

After a month of using it the following patch proved to be useful.
It adds anew new defcustom delete-pair-blink-delay based on the default
value of blink-matching-delay.  Exactly the same defcustom is also
added copy-region-blink-delay for the feature request in bug#42865
not to blink when copying a region: