I don't think that makes 100 / 100 the most likely result if you flip a coin 200 times. It's not about 100 / 100 vs. another single possible result. It's about 100 / 100 vs. NOT 100 / 100, which includes all other possible results other than 100 / 100.

You can tell the difference between

93 heads, 107 tails and

93 tails, 107 heads

but not between

100 heads, 100 tails and

100 tails, 100 heads.

So while those are two results (93/107 and 107/93), they really only count as two separate outcomes if you pre-specify that the first number is heads.

If instead you consider symmetries, where there are 2 ways to get 93/107 and only one wall to get 100/100, then you have more likelihood for the 93/107 outcome because you have two ways to get it.

Depends what you count as a result, I guess. "There is exactly N flips of a single kind" is also a viable definition, just as "The exact sequence of flips was x_0, x_1, ... x_199" is.