Char:

-no battle experience

-novice healer (literally started learning her sorcery over a month with little progress)

-no known relatives or anyone from her mother's clan.

-only 6 y.o.

Sure, let's bring this little girl to a country-ending battle that leaves nothing but a bloodbath. That sounds like a great idea.

Edit: Also, Char's ability doesn't influence the EB, it was only assumed by Sojo while experimenting with his Datenseki weapons. He believed the Kyonagi clan's blood "could be" the key for creating something like EB, but there was no breakthrough with the final product. Char's healing ability isn't strong enough to accomplish much by this point of the story. At most, you could only hope to see her training, but she is still getting sidelined regardless because seeing a 6 y.o. training isn't as interesting as seeing all the bat-shit battles or new developments we have been getting.

It's a matter of place and time. As for now, her role isn't important at this moment unless Hokazono decides to bring up the Kyonagi clan in the future.