The downside to sphere tracing and similar is that it limits the input model: you have to guarantee that evaluating the model at [x, y, z] gives you a result that's less-than-or-equal to the true (Euclidean) distance to the shape's surface.
(or a distance adjusted by some constant scaling factor, i.e. Lipshitz continuity [2])
This is a relatively fragile property, and really limits what kinds of shapes and transformations you can use when modeling.
Using interval arithmetic is more robust against arbitrary models, at the cost of being less efficient when models are well-behaved.
I don't know much about state-of-the-art fractal rendering! I'd imagine that the fixed (original) tape in MPR would be a limitation here, because you may want to terminate conditionally, rather than evaluating a fixed expression.
[1] http://www.fulcrum-demo.org/wp-content/uploads/2012/04/Cone_...