The minhag is that we wash for karpas and eat less than a kezayis.
The reason is that when one eats a wet food, he is required to first wash his hands.
Question: While it is true that one who eats a wet food needs to wash, it appears to my limited understanding that this is only if he will be eating a kezayis or more.
If he will be eating less than a kezayis, there is no need to wash for 2 reasons (sfek sfeika): (1) There are opinions that nowadays there is never a need to wash for wet food; (2) There are opinions that one who eats less than a kezayis of BREAD may eat it without washing; how much more so by a wet food, where according to some opinions there is never a need to wash! I subsequently discovered that this is the opinion of Chacham Ovadia Yosef in Halichot Olam, Helek 1, Parashat Tazria that one who eats less than a kezayis of wet food is exempt from washing his hands.
So the question is, why do we wash by the seder, given that the minhag is to eat less than a kezayis of the karpas?
These are amoung the reasons that we don’t say a bracha. However, we keep the minhag, to make the children ask, and other reasons, in part because this is what they did in the time of the Bais Hamikdash.
See OC:H 473-6, M:B 53, Chayei Adom, Hilchos chag behag Pesach 24 ftnt 15 from MOrdechai Seder pesach Hakotzair.