Why rely on climate models as opposed to paleoclimate data?
We need both paleodata and models, in fact the relationship between paleodata and the climate at a certain time is typically evaluated through models. Paleodata does not actually measure climate observables directly (tempreture/pressure/salinity/other) but instead is (e.g.) a geochemical quantity related to one of those. 

For example, the two most frequently used records are the Antarctica EPICA ice core record and the Lisiecki Raymo benthic stack. The isotopes in these records are affected by temperature at a point on the planet and global ice volume, but how that relates to global temperature and the size of individual ice sheets requires inference from climate models.

Further, climate (or earth systems) models can allow us to probe what could happen in addition to what did happen. Current CO2 levels are reaching a point not seen in the ice core record (our most direct records) and so we need increasingly complex models to get a handle on the range of possibilities.