To further muddy the water.....
As to LNAV it may have worked with a steeper descent gradient but that would require a second IAP (Y and Z), which the FAA presumably didn't want to do at this location. Or some obstacle to the left or right of the ILS/LPV lateral areas caused LNAV too steep to meet criteria.
Here's an example of a runway (KRIL 26) with separate plates for an LNAV procedure (with CTL) and the separate WAAS LPV. Of note, the descent gradient for the LPV (3.60) is steeper than the gradient for the LNAV (3.58).
No one size fits all in them thar hills....
http://155.178.201.160/d-tpp/1305/06741RW26.PDF
http://155.178.201.160/d-tpp/1305/06741RX26.PDF
(Once again, the LPV to WYS 19 is the
ONLY IAP to 19, no LNAV. I think this is probably somewhat unique to find a runway ONLY served by an LPV line of minima, nothing else. I'm also wondering then why 19 couldn't be served with an LP line of minima with CTL which might have to be higher than 8240 as a result of the LP approach mins possibly being higher than 8240 on that end?...once again creating a problem for said Captain)