I would like to suggest the following answer to your question. It comes from all the information in the Bible on this incident, not just those parts pointed out to us about Jacob and Rebekkah's deception.
Why delay a blessing by asking for food?
I would like to suggest that there were more deceptions involved in this story, than the ones plainly pointed out by the text, and like a good mystery novel, the plot thickens as the story proceeds.
Essau was married to local women who we are told, were not worshippers of God. We also learn that Essau treated his birth right with contempt, holding it of equal value to another stew or pottage that his brother prepared, which may also have been a planned deception by Jacob, or part of the second plot that followed it.
We learn that Rebekkah was unhappy with the women and their families that Essau married into, and the reason given was that these women did not honour the true God. This she told her husband Isaac, in the form of a complaint, and as a reason for Jacob to quickly get out of town, after the two had finished their deception and obtained the Blessing.
We also learn from the text following this part of the story, that Isaac lived on for many more years, after this incident, which may have taken place when he was about 100 or perhaps 140. He was nowhere near death, and lived to the ripe old age of 180 years, 40 years past this time of the Blessing.
If his health was 'so poor' that he said he might die soon, why is it he lived on for another 40 or 80 years past this time? (the plot thickening)
From the Bible writers we learn that Essau was 'hated' by God, while Jacob was 'loved'. The text says this was before either had done a thing. However, God knows the end before the beginning and knew both boys and what they were each like, before they were born.
The key thing about this story is that while Essau treated his birth right and the Blessing of Abraham as 'nothing much', Jacob desired it so badly that he was willing to risk his life to get it, and did, along with scheming in a couple of different plots of deception.
This is the thing that God valued, (not the deception and character failure) He loved that Jacob wanted the Birthright and Blessing enough to risk his life over it. On the other hand God hated that Essau thought so little of it that it was only equal in value to
a bowl of soup. Essau gave up spiritual inheritance over fleeting physical gratification.
What I want to suggest is that God Himself was running His own plan, prophesied to Rebekkah at the birth of Essau and Jacob (twins)and that was that Jacob would inherit the Blessing and Birthright, and He was behind Jacob receiving the Blessing.
Although the text seems to suggest that Isaac seemed satisfied that it was Esau who he was blessing, I would like to leave this food for thought, that Isaac lived almost a half century past this event (and maybe even double this amount of time) although he rushed to give the Blessing because he said he was facing his own demise, Issac may have been running his own deception, with full awareness of the plot of his wife, and He may have calculated to give the Blessing to Jacob, because of Essau's behaviour that showed he did not value the things of the Lord.