MWI is exactly as simple mathematically as CI, so not sure what you mean by "simpler".
MWI still postulates the equivalent of wave function collapse, but instead of it happening only for the quantum system being measured, it is happening in the mind of the observer, as each "version" of that mind gets entangled with a single "version" of the outcome.
Even if you were to accept that this process is more natural (so not an "assumption") than wave-function collapse in principle, that simplicity completely falls apart when you then need to recover the relationship between the probability of observing a certain outcome and the amplitude of that outcome in the wave-function.
CI just says "when a quantum system described by a wave-function interacts with a measurement apparatus that measures in a certain basis, the wave-function gets updated to one of the values of its decomposition in that basis, with a probability equal to the modulus of the square root of its amplitude in that basis". Of course "measurement apparatus prepared in a certain basis" does a lot of work here, as we don't know how to define this in terms of a quantum system.
To make a similar quantitative prediction, MWI needs to define something like "the number of worlds", so that it can then say something like "when a quantum system interacts with a measurement apparatus prepared in a certain basis, the measurement apparatus becomes entangled with the quantum system such that for each value of that basis state there is a number of worlds proportional to the square root of the amplitude of each value of the decomposition in which the apparatus sees that particular value; if we were to compute the probability that we happen to live in a world where the apparatus is showing the value X, that probability would naturally be higher the more worlds there are where it shows this value X". So, the MWI has to actually introduce extra elements (the worlds and their number, and the observer wanting to compute a probability) to explain the actual measured results of quantum experiments.