This has actually been done before. There was a series of Justice League of America novels
from Pocket Books about a decade ago, but all but one of them were solo books featuring Batman, Wonder Woman, Flash, Green Lantern, and Superman respectively. Only the last one was about the full team.
I only read a couple of them, but the solo ones I read still featured the team prominently. They only put the hero from the title in the most prominent role.
The final one is my favorite superhero novel and one of my favorite JL stories of all time. No relevance on the topic, just putting it out there.