Why not make the Rift symmetrical? It will eliminate all of the differences between the two sides so that there's not an advantage to one side (dragon is closer to blue team, red/blue buff locations, camera angle, bushes) and make it so you actually can just flip the camera to make it look the same on blue and purple.
It is symmetrical, just not plane symmetry. Its symmetrical about the origin, instead of over a line. In fact, the symmetry that riot used making SR makes should make it super easy for them to switch camera angles. BUT The problem with camera angles is how the game is written; rendering the Rift from another angle might be challenging. In fact, if it were how I would do it, (I'm lazy in my design) then Summoners's Rift is actually a 2D image with 3D characters and trees sticking out of it.
It's not actually possible to make the map symmetrical and have 2 unique features. The only place to put a unique feature and still have symmetry around a center line is dead center in the map. You can't put both baron and dragon dead center. If there was only one unique feature, you'd have to have 2 lanes or 4 lanes to have symmetry. If you replaced baron and dragon with a pair of identical monsters (bagons?) you'd have to eliminate the river or weight the map heavily towards top or towards bottom. If you replaced the baron and dragon with 4 identical monsters or two mini-dragons and two mini-barons (and so could preserve the river), you'd have a very crowded jungle and remove the whole idea of dragon and baron fights - if there were more of them they'd have to be weaker and not as important to contest, and teams could just go take their version instead of contesting for the only one.
Any of these choices would dramatically change the nature and strategy of the game and shouldn't be approached lightly.
In any case, having a feature-symmetrical map and rendering a map from two different angles are entirely separate problems. Making the map symmetrical wouldn't make it any easier or harder to render the map from the opposite point of view. The problems there are around making sure every terrain feature looks good rendered from both sides and that everything looks reasonable from both sides. Also possibly issues when champions are in front of map features or vice versa, that everything is still sensibly in view. Tall terrain objects are a problem here because with one camera angle you just put the base of a tree at the lowest non-passable map point and make it tall enough to just touch the highest non-passable map point. There's a blank space behind the tree that nobody ever sees. If you just flip the camera angle, you have plain ground (or empty space with no art at all!) that you can't walk on, and the tree obscures passable terrain. You either have to move the position of terrain objects so that players see different but sensible art obscuring only impassible terrain, or you have to have only very low height terrain objects, your dwarf trees centered in the impassible areas and low-lying brush or rubble marking the rest of what's impassible. (Or you can keep your tall terrain and simply have it possible to walk behind terrain objects, but that leads to being able to hide in ways that aren't intended by the vision mechanics. Usually in games where terrain objects can obscure active gameplay objects, you can freely rotate the camera so you can always get a good view angle, but I don't think anyone wants to try to manipulate camera angle in the middle of a teamfight in this game... at least I don't.)
tl/dr: it's not that simple.
