I live in Mattoon, IL and we usually take I-57 down to Southern IL, then switch off onto I-24, then catch I-75 at Chattanooga, then take 75 all the way into Florida, then get on the Turnpike, then catch I-4 for the final few minutes of the drive.
Like other posters, I think this route is better than the route you're proposing, but I did take that route home on our last trip. Going through Georgia on the way there, I noticed massive traffic backups just outside of Atlanta on the Northbound lane. We were going South, but I didn't want to take the chance of massive backups on the way home, so I opted to take I-10 through the panhandle until we get to highway 231, then up to Montgomery and catch I-65 into Nashville. Mileage-wise, I think it was probably a longer route. But for us, it seems like no matter what year we go, we always run into major roadwork and traffic backups on I-75 (not due to Atlanta rush hour, but due to all that traffic being bottled up into one lane due to the roadwork). And I'm the type of person who would rather go the longer route and at least know that I'm moving and heading somewhere as opposed to taking the shorter route and sitting idle in traffic for God knows how long. And in this case, even if that route was an hour or two longer, by the time we would have wasted an hour or so in traffic backups going the I-75 route through Georgia, we wouldn't really be out any extra time anyway.
So long story short, all other things being equal, the way you're proposing isn't any more efficient and would not be my first choice. However, if you're just looking for a new route for a change of scenery, or if there is major roadwork going on which may cause you to sit in your car moving 5 MPH for 45 minutes on I-75, it may be worth considering taking I-65 through Alabama instead. Otherwise, you're better off taking I-75.