The most common and most likely answer to this crossword clue is the 7 letter word SPEARED
I've seen this crossword clue in Independent
S
P
E
A
R
E
D
More clues leading to the result SPEARED
Buddy explains!

The straight part
We know that "Drove home point" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case drove home point = speared.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SPEARED mean?
SPEARED verb- To pierce with a spear.
- (by extension) To penetrate or strike with, or as if with, any long narrow object; to make a thrusting motion that catches an object on the tip of a long device.
- To shoot into a long stem, as some plants do.