Why are there no RNAV (ILS) approaches?
You are confusing some terminology.
RNAV (GPS) approaches can have several different sets of minima.

See the example RNAV (GPS) Y 28L at O'Hare:

It has:
LPV
LNAV/VNAV
LNAV
sets of minima.



LPV is an instrument approach procedure (IAP) with localizer-type precision and with vertical guidance, (hence the name LPV), provides a pilot with a "ILS-style" approach complete with a decision altitude (DA) but using GNSS equipment instead of VHF equipment like that used for an ILS.  Usually the lowest weather minimum of the 3.

LNAV/VNAV is another line of minima with baro-aided (altimeter-based) vertical guidance including a DA but the weather minimum is usually a bit higher than LPV.

LNAV-only is the least precise of the 3 and is a non-precision approach, no vertical guidance, includes a minimum descent altitude (MDA) instead of a DA.  This is a "dive &amp; drive" approach similar to Localizer or VOR approaches.  Normally has the highest weather minimum due to the nature of non-precision approaches.

There are RNAV (GPS) approaches and there are ILS approaches, but there are no RNAV ILS approaches.

Note: There might be a rare exception to this as described in appendix C of FAA Order 8260.58A CHG 2: If the aircraft/aircrew/airline are performance-based-nav (PBN) capable &amp; authorized there could be an IAP constructed with a radius-to-fix intermediate segment leading to an ILS final segment, whereby, the crew would navigate with GNSS equipment on the RF segment and then transition to ILS equipment for the final segment.  I would say in my experience this type of approach construction from the US TERPS is very rare.

I will add that WAAS is to LPV as GBAS is to GLS.  GLS is only available at 2 airports in the US, while RNAV approaches with LPV minimums are available at a great many US airports, adding a "ILS-like" utility to those airports without incurring the infrastructure cost of adding the ground equipment necessary for ILS approaches.

WAAS capable GPS receivers are prevalent; while very few aircraft (the Airbus A350 is one example) have GBAS capable GPS equipment.