It was an immigration bill under Speaker Fraser, I believe, in 1988.
First, splitting an omnibus bill is the decision of the government. It's a political and policy decision as to how it's packaged, and it remains a political decision as to whether it will be split. The House may agree to split a bill or send two parts to different committees. That's possible, but it has to be a decision of the House.
I won't comment on the substantive part of your question as to whether it is desirable. It can be a very efficient way of proceeding, but it can make it difficult for a member to cast a single vote on the principle of the bill or on third reading.