Refining is a cash cow and although it has it's ups and downs, does not require a lot of capital to run. They are using that cash flow to expand the other business, plus they are going to export a lot of product over time as demand in the US wanes. I could definitely see them selling the east and west coast refineries.
They cannot spin it off. If they want to get rid of chemicals they would first have to offer their half to Chevron and I seriously doubt they would get what it is really worth. Also it is a good fit with their other businesses. It is no accident that refiners are in chemicals and that the original plants were on the same property. A product of refining, primarily naphtha is a feed stock. used to produce Olefins a large CPChem product.
LYB might be a better comparison than the 2 you mention. I have not done an in depth study of LYB's product mix but on the surface it appears that it is a majority of olefins and polyolefin's. That business is the one PSX is expanding.....BIG! The PSX midstream segment largely provides the feedstock for for the olefins business. Refining is going to shrink as a % of the total even if PSX holds all of the presently owned refineries. The PSX business plan seems to make a lot of sense.
A different question, in the same vein, might be whether or not PSX should buy-out the CVX 50% share of the chemicals business.
NO, they should not. Too good a fit for PSX. Part of what sets this company apart from your "normal" refining company. Major midstream operations is another part of the company that is in growth mode and again sets PSX apart from the rest.