People (I) use the cage for a reason. It's not because a cage adds to the visual appeal of the plant... but it's not as if other gardeners are coming around to make fun of the way my tomato plants look.
The plant is gonna get huge, and the fruit bunches weigh a ton on the branches of the plant. Even using a cage and plant ties, I often get entire branches breaking at the main trunk of the plant. I'm sure you can pull it off with stakes, but it's going to take a LOT of them, and they'll need to be supported laterally (like, tying them to one another... like a cage!).
BTW, the cage needs to be installed when the plant is small... small enough to get the base of the cage around the plant... so it might be too late anyway.
The roots are plentiful. I wouldn't worry a lot about taking some of them out with the stakes.