what should be your goal when completing a crossword?

about a week ago I suddenly awoke with the need to play crosswords. 2 days ago I purchased the NYT strictly medium. I had been playing online crosswords and doing pretty decent, but the cultural references in this one really throw me off and seem to be meant for people who simply aren't me. I have to look up a fair bit of answers, more than I like. At this point I wonder what hte point is in playing if I have to keep searching stuff up.

When playing crosswords, do you play to learn new facts, people, things etc, even if that means searching stuff up? or should it be about trying to avoid google as much as possible, even if that means spending weeks on the same crossword?

For example, Sarges superior. i thought about the comic beetle bailey for a while, and couldnt come up with the name of the guy. so ilooked up the characters and nothing fit either. so i just looked up the answer I got so frustrated.

I'm not sure what I did was the spirit of the game or not. Is it about learning at whatever means, or struggling?