Why are changes to non-current assets and liabilities not included when calculating LFCF or UFCF?

So the formula I've been taught for: UFCF = EBIAT + D&A - CapEx + changes to NWC LFCF = NI + D&A - CapEx + changes to NWC

However, when you actually build out a cashflow statement and get to ending cashflows for the period, you would also include non-current assets and liabilities for Cashflow from Operations. Why isn't this included in computing unlevered free cash flow and levered free cashflow for that matter? Don't these line items both affect FCF? Further, is LFCF different from ending cashflow that is computed on the C/F statement? Seems to me starting point for both is NI as that already takes into account interest expenses paid out...

TLDR: why choose specific line items from the cashflow statement as opposed to analyzing all of the line items for each section (operations, financing, investing)?