The e in eDRAM doesn't really mean DRAM embedded in the cpu, it means DRAM embedded inside a logic process.
Modern DRAM chips are manufactured in an entirely different way on a very different process than logic chips, and the manufacturing processes are incompatible. eDRAM was a very different implementation of DRAM that could be manufactured on a logic process.
The difference between eDRAM and DRAM is not just that eDRAM is closer, it was also typically dramatically faster, but also had shorter retention period requiring more frequent refresh.
Modern DRAM chips are manufactured in an entirely different way on a very different process than logic chips, and the manufacturing processes are incompatible. eDRAM was a very different implementation of DRAM that could be manufactured on a logic process.
The difference between eDRAM and DRAM is not just that eDRAM is closer, it was also typically dramatically faster, but also had shorter retention period requiring more frequent refresh.