Eastern-rite Cardinals are rare for two indirectly related reasons. The first is that historically speaking, Cardinals represent the nominal heads of principle churches in the city of Rome. They were close advisors to the Latin Patriarch (the Pope), and elected the Pope on behalf of the Latin clergy.
Many Eastern Catholics recognize another as their Patriarch, who is himself in communion and obedient to the Pope. It is thus awkward, in a formal sense, to appointment an Eastern Catholic bishop as Cardinal, as he would then be an advisor to the Pope, and his Patriarch. I believe this is partially mitigated by appointing the Patriarchs themselves as Cardinals. Their personal position as head of an Eastern Church outranks therir position as Cardinal, but they are thus permitted to participate in the Papal conclave.
The lessor reason there are few is that there are 100 times fewer Eastern Catholics than Latin Catholics (13 Million, compared to 1.3 Billion). There representation will always be limited by this proportion, irrespective of difficulties of conflicting ranks within multiple ritual churches.