OK, let's do the math here.
Given a 2.6 mm x 11.0 mm die, you can obtain 2177 dies per 300 mm wafer. If TSMC N3 defect densities follow the trend established by N7 and N5, we would expect around 0.11 defects per cm² at the beginning of the HVM ramp. Using the Seeds model, a 28.6 mm² die would see a yield rate of 96.95%, or 2110 fully functional dies per wafer. At a cost of $20,500 per finished wafer, each GPU die would cost Intel $9.72.
Just the GPU slice (not including media block or display engine) for ADL 8+8+1 is 16.64 mm². That's for 32 EUs on Intel 7, so 192 Gen12 EUs would work out to ~100 mm². You can fit 626 9.0 mm x 11.0 mm dies on a 300 mm wafer. A 99 mm² die and a D0 of 0.10 would result in a 90.99% yield rate, or 569 fully functional dies per wafer. A finished Intel 7 wafer would have to cost $5,500 or less to compete with TSMC N3.
Notebook PC platforms are Intel's iPhone. They generate more revenue and profit for Intel than any other product they produce. Intel currently has locked in customers for ~130 million U Series chips with IGPs annually vs. 0 for desktop discrete GPUs. A best case scenario for Intel would be reaching something like 8 million dGPUs in 2023. The first Arc products, slated to ship in Q1'22, are based on the Alchemist GPU which is being manufactured on TSMC N6. It is incredibly unlikely that the follow up, Battlemage, will be a Q1'23 product made entirely on TSMC N3. However, a 192 EU tile at just 28.6 mm² that could be used for both IGPs and dGPUs is a perfect lead-off product on a new manufacturing node.