The idea behind changes in working capital is that when you value (or buy) an entity, you are buying the company on a going concern basis, able to support its own operations. if you agreed to purchase a company for $100 and it turns out that you still have to put in $10 MORE because there was no working capital left on the books, then in essence, you really paid $110 for the company. Thus, in purchase agreements, there is always a negotiated and agreed upon working capital requirement. In the case of FCFF, it's the same concept - because you have to continue to support your operations, this reduces the amount of cash that you can receive, that is, the amount of "free" or "excess cash generated" is reduced by this obligation.
If you agree that Inventories should be part of the working capital calculation, then you should also see why A/P and A/R are. They are due to operations; in the case of A/R, you sold good (sales) but haven't yet collected and yet, you need to pay your suppliers & vendors (COGS) and thus, those are all cash impacts, the net of which is the change in working capital. Just like you have to buy inventory to support COGS & Sales!!
Please don't overthink it. A/P is NOT an interest free loan or borrowing, it is trade credit. You are correct in your assessment of A/R being earnings in transit and thus, unless you collect immediately on everything you sell, you will have to support that trade credit to your customers; hence a working capital item required to support day-to-day operations. A/P is the same concept, but reversed. Thus, both are included in working capital cahnges.