I have a good King KR87 ADF in my airplane, and for an approach in which the LOM is an IAF, it's a whole lot easier to use the separate ADF than to do the knob twisting necessary to use the same GPS box for the approach which you're also using it for the ILS.
On this particular approach, let's assume that you were coming from the east toward OTH VOR at 6000'. As you're almost there, you're cleared for the ILS 4 approach. Assuming you've had the OT NDB tuned in on the ADF, you just turn the airplane to center the needle to fly to the OT LOM, with your GPS/VOR tuned to the I-OTH ILS. When the ILS comes alive, you turn outbound on the ILS, start down from 6000' to do the procedure turn, and come back in onto the iLS. As soon as the ADF reverses, you tell Tower that you're Emire inbound. Meanwhile, you've watched the distance on either the GPS or DME so that you waited to do the procedure turn until you were at 2000' and started descending to 1000' as soon as you're wings level out of the procedure turn, to intercept the glideslope before you get to OT LOM.
But do it again, this time without an ADF. You're almost to OTH VOR when you are cleared for the approach. Yeah, you can tune in the LOM location on the GPS, but that means switching it from the VOR to GPS and then back to VOR again to intercept the ILS. Not too difficult, but more difficult than if you have an ADF.
Now try to do it without a GPS or ADF or DME. All you have is navcoms. You are cleared direct to the LOM before you get to OTH. That's the IAF, so you have to get there somehow. The only way that comes to mind to do it accurately is to continue to OTH, then turn on the outbound 241 radial until it intersects with the ILS, then turn outbound on the ILS. That's fine if you have 2 working navcoms, but involves a whole lot of knob twisting if you only have one. If you have a marker beacon receiver, you'll know when you've arrived in the vicinity of the LOM, but if you don't (and it's not a requirement), you have no way of identifying the LOM, outbound or inbound, other than by centering the 241 radial on a navcom.
So while the approach probably could be flown with only a navcom or two, having an ADF would make it much easier and safer. Perhaps the "safer" part is why it's required along with a DME (or an approach certified GPS in lieu of the ADF & DME).
Cary