The numbers are sent in this peculiar format, because that's how they are stored in the certificates (DER encoding in x509 uses big endian binary), and that's the number format that OpenSSL API uses too.
It looks silly for a small value like 65537, but the protocol also needs to handle numbers that are thousands of bits long. It makes sense to consistently use the same format for all numbers instead of special-casing small values.
It looks silly for a small value like 65537, but the protocol also needs to handle numbers that are thousands of bits long. It makes sense to consistently use the same format for all numbers instead of special-casing small values.