If you use public clouds for rarely use SW/HW then it is more economical. You can use your private cloud where privacy is more important than cost. So hybrid cloud is more economical and secure.
Not sure your operational definition for hybrid cloud is e.g.
1) a company's users access to both private cloud and public clouds at the same time e.g. private cloud IaaS for project campaigns / apps development & using public cloud SaaS Gmail for email etc., or
2) using a private cloud as cloud service broker / platform to connect to external clouds to ingest their services e.g. AWS, Rackspace, Azure etc. Another words, your users can access other external public / private cloud services via your private cloud.
Based on your description, more like the latter definition (i.e. no. 2) in which you don't need a hybrid cloud because your private cloud already have the external cloud connectors that you can connect to other external cloud services. However, you need to ensure adequate labor efforts to integrate different cloud service offerings subscribed (e.g. AWS, Azure etc) with your private cloud, AD / LDAP integration for authentication, DHCP services for IP address assignment, obtain access credentials for those cloud services, setting up needed FW, LB, DMZ & VLANs etc.
If your definition is the former (i.e. no. 1), think may not be relevant in this case because the company users can access various private / public clouds that they want to subscribe. However, this may not be a good sign - because each Line of Business (LOB) tries to setup their own clouds & end up creating cloud sprawls. I encountered such customers in which ending up to perform clouds "consolidation". All the best.