Up to you. You are a Instrument Pilot. Are you active GA IFR?
How many airports can you land at with just a VOR? Just ILS (with no DME)? With LPV RNAV GPS?
The answer is VOR few and less everyday. The FAA will always keep a few for MON (Min Operational Navigation).
Even airways are going from Victor to "T" or Tango airways (GPS based). It does not matter you can sub a GPS for DME and VOR.
Just lost another VOR in July and airway went from Victor to Tango with a new waypoint over where the VOR is / was.
ILS? I have a soft spot for ILS. So familiar no GPS or data base, but you will notice many require DME (or RADAR) as well (due to MB/NDB/LOM going away)
As stated if you have a GPS, TSO certified for terminal/approaches GPS can sub for DME.
If you fly for airlines ILS is still king for a few reasons.*
LPV. Every airport has LP or LPV RNAV GPS approach. Many airports that is only approach.
Ones with VOR/LOC and ILS almost always also have a LP/LPV in my experience and area.
I only have a Garmin GPS 175. No VOR/LOC/GS/MB/ADF/DME... I can do LP and LPV and enroute.
If you are going to train in your RV than get VOR/LOC is needed. You don't need ILS (GS) for training/check ride. LPV is a substitute for a ILS precision approach for training/check ride ONLY. However out in the wild, for filing, alternates, etc. LPV is considered a non precision.
Mins? Yes LPV can be 200-1/2 and I have one at nearby airport. My airport is about 300-1. Is that going to make a difference. I pick the WX I fly in.
Also ILS has one trick up it's sleeve.*
* ILS Cat 1 is 200-1/2. ILS and LPV can share same landing Mins 200-1/2, but the ILS has one advantage in that FAR's, which allow pilots to go below DA with ALS only to 100 HAT. That doesn't apply to LPV. They may change that but the reason is LPV does not REQUIRE an ALS like an ILS. The "S" in ILS is for SYSTEM. Question, important, what are you doing single pilot, single engine IFR down to 200-1/2 or 100-1/2 to land?
LPV rocks. If you can't get in with typical LPV you are doing it wrong (meaning flying in weather that is too low).
One part that makes the ILS "system" is ALS. LPV does not allow the 100HAT on ALS only. One reason LPV does not have ALS requirement. May be they will change it to include LPV approaches overlaying an ILS runways with ALS. As you know you lose ALS components your ILS mins go up. LPV approaches are at mega, large, medium and small airports, but at small rural airports LP and LPV are almost exclusively only approach they have.
Airlines will use ILS in part for the 100 below DA with ALS only, crew training and consistency. I do not think ILS (or VOR) will be gone for the foreseeable future. BUT an ILS is only at larger airports and LPV is EVERYWHERE ILS is and more. .
Bottom line. You can get by with a RNAV GPS with Approach/Terminal TSO alone. But you can NOT get by with VOR/LOC/ILS only without GPS or DME, and even then you are limited. No LP, LPV or T airways. It really is a no brainer. One of the new fangled GTN650/750 is the full meal deal. If you can afford it and hard ball IFR dude, go for it. They are nice. If going casual occasional IFR, one of the Garmin GPS units, GPS only, GPS/COM or GPS/Transponder may be best. For me I have VOR/LOC/ILS on a hand held as a novelty.