The 24 hours period for awarding bounties is designed mainly to attract attention to a question, rather than recognizing someone's great answer. This is why there is a waiting period, it's because of the way the bounties feature was designed. Bounties are seen more as a last resort for question that either requires more research and effort or needs a last chance before it's forgotten.
From the meta post mentioned in the comments:
The bounty system is specifically made to draw attention to a question
and rub people the right way into answering it. The reason there is a
period in which the bounty cannot be awarded is to allow people to
spend some time into providing a great answer -- which sometimes
requires some thought and research. If a bounty is awarded quickly, it
discourages other potentially better answers -- people would be
significantly less inclined to provide a great answer to a question
for which the bounty has already been awarded.
Another reason for some seemingly unnecessary restrictions on the
bounty system (i.e. bounty amounts, maximum number of outstanding
bounties at any particular time, bounty times etc.) are there to
prevent abuse, for example continuously transferring some of your rep
to a buddy of yours.
So, I think it's good to add bounties as a recognition of effort, but because they were designed with other uses in mind, there are limitations to it (the 24 hours waiting period being the main one).