Think about it.
A cell eats a little nutrient and a little food. It wants to procreate. It splits. Using the supplied foods it has, the next cell will be able to use those same foods a little better. The new cell does this same thing. Now this continues for several generations with each new cell being able to use the foods that are available to it better than the previous.
To simplify the numbers lets start with 1000 cells into a starter of cane sugar.
1,000 = Malt eaters
2,000 = 1st split
4,000 = 2nd split
8,000
16,000
32,000
64,000
128,000
256,000
512,000 = last split
-----------
1,023,000 = Total cells
- 1,000 = Original Malt eaters
------------
1,022,000 = Slightly mutated non-malt eaters
By the time they you get to 1,023,000 cells, only the first 1000 are 1st generation malt eaters and the rest mutate to like cane sugar a little bit more each split.
You pitch that into your wort and those 1,022,000 suddenly get a whole new food source.
Best case, you have a little more lag time.
Worst case, you get a totally different tasting beer.
The purpose of a starter is to raise a nice crop of yeasties that are ready and eager to chow down on your wort.
Simple logic says use wort, not sugar, not honey.