I don't see why the number of how many times something exists must equal how many times something is observed.

Those numbers don't have to be equal. They only have to be equal in a "many minds" version of "many worlds", where observations are all that exists anyway. More precisely, in Many Minds, the only branching you care about is the branching of observers, and the only "parts of the whole" that are given existential status, are parts of the wavefunction which correspond to experiences. So you never speak of just having "an electron in a spin-up state", but only of "someone observing an electron in a spin-up state". Clearly a viable many-worlds theory must at least have the latter - it must at least say that branches exist in which observers are having distinct and definite experiences - or else it makes no connection to reality at all. But to ascribe reality only to observer-branching, and not to the branching of lesser physical systems, is a remarkably observer-centric ontology; it's hard to see what advantage it has over "consciousness collapses the wavefunction".

In any case, the real point here is that you can't defend the "no definite number" argument by constructing a contrast between observation and existence, because observers and experiences themselves exist. In a Many-Worlds context, the observer is not outside of physics. The observer has a physical state, the experience is a physical state. You use the expression, "how many times something is observed". How can that expression have meaning, unless observations exist, and exist distinctly enough to be counted? So if you're in a Many-Worlds ontology and counting experiences, but you insist that worlds can't be counted, then what exactly are you counting? Where are these distinct countable experiences located?

I don't like it being called "existing more" either ... but "observed more" or "experienced more" are good enough for me.

If A is observed, then A has an observer; when you say A is "observed more" than B, you are saying that the observer of A "exists more" than the observer of B.