Do you really believe that going IFR is no safer than VFR and that there are no considerable benefits to going IFR even when the weather is good?
...and you couldn't make the same call with your position VFR?
You certainly could. The problem is, most pilots, especially low time pilots over the mountians for the first time, will be busy flying the airplane, trying to fix the problem, and focusing on finding a landing spot. I know this because I was once that low time pilot, over the mountians, in a single, when the engine failed. A radio call was the last thing on my mind. Sure it should have been, but the simple fact was that it was not.
Because we were IFR, ATC questioned why we no longer at 15,000 and we were able to declare an emergency sortly before losing radio contact. Had we been VFR, we would have dropped off of the controllers screen and he probally would not have given us a second thought.
So now let's throw the NORDO scenario at it. You are NORDO on an IFR flight plan and go down. They don't know you're down until you don't show up on RADAR again. Same thing VFR. They don't know until you don't show up and close your flight plan. You're still going to be sitting in the shade where it's 100*F thinking "Maybe I shouldn't have flown over this kind of terrain...".
There are many differences between VFR and IFR in this situation. IFR they will launch a SAR in a relatively short time if you do not show up. VFR will they call the FBO a few hours later. If the guy says "Oh yeah, I saw a red and white Cherokee land, they are here" (which happens a lot), you are screwed until your family gets concerned. There very few routes from CA to TX that do not involve flying over some sort of inhospitable terrain.
Unless the OP has O2 in the plane, going IFR could be problematic in that part of the country. Some of those MEAs are up there. Going VFR you can just go around the hills. No one says you have to fly in areas of no radar or comms coverage. Just pick up VFR flight following when able and if they're too busy, monitor their frequency anyway.
Again, if you are just randomly picking your way around the hills, it will be very hard for the SAR teams to find you. If you cannot meet the MEAs then IFR is not an option and this entire discussion is moot.
Not to mention. A plane you don't know. Gyros that who knows how reliable they really are? Do you really want to be tempted to pop through a layer thinking "I'm on an IFR clearance/flight plan anyway" only to have the joy of cruising over the mountains partial panel avoiding ice while you're trying to find yourself a place to land?
Flying IFR and in IMC are two completely different things. I flew over the mountains in IMC 8 hours before the engine quit on my flight. Had it happened then there is no question in my mind I would be dead. I will never advise flying a single in IMC over that kind of terrain.
Alex.