When training a neural network, you usually play around with the architecture and need as much flexibility as possible. You need to support a large set of operations.

Another factor is that training is always done with batches. Inference batching depends on the number of concurrent users. This means training tends to be compute bound where supporting the latest data types is critical, whereas inference speeds are often bottlenecked by memory which does not lend itself to product differentiation. If you put the same memory into your chip as your competitor, the difference is going to be way smaller.