Intel could try to use HBM in order to drive further investment into production with the long term goal of reducing costs so that it is affordable for consumers. It obviously won't replace GDDR or DDR across all segments, but I can see Intel wanting to produce something that could be considered an x86 SoC where everything is combined into a single package, which makes a compelling product.
They know that AMD wants to develop that kind of product (see that old concept where they had a server chip with Zen cores, GPU chiplets, and HBM memory all on a single chip) so it's something that they need to test out and consider as well. Intel already has a little bit of experience with this in Hades Canyon which included HBM for the Vega GPU that was put on package.
I think it's fair to say that they have some interests in HBM and that it's not impossible to imagine them using it in some products.