Any aircraft trying to fly an approach without the equipment and fuel required for the approach is SOL from the start. However, I would just fly the approach using GPS in OBS mode. Now if the ADF goes down, then who's having lunch?
Well, if you're doing that and there's not an overlay that allows that, then you're violating the regulations. While that is definitely a good backup in case you do have an ADF failure and it becomes an emergency (at which point you invoke 91.3), it's not a good idea to make a habit of violating the rules.
Re Protected airspace: Let's say you have an engine failure, or you're on vectors near terrain and loose radio contact, or you are departing an airport in uncontrolled airspace at night, or you are denied a night IFR departure and have to go out VFR and stay low to avoid airspace (like in Phoenix recently), or...
Let's look at each of those situations differently. Your first couple (engine failure, vectors near terrain and lose radio contact) are emergencies. That is where extra tools are very useful for helping you turn what could be a very bad day into just a mildly bad day. So here, it enhances your ability to deal with the situation.
Departing a non-towered airport at night (or flying uncontrolled airspace at night) would be more of a normal operation during which the tools are definitely an aid. However, they are no substitute for following the legal, established procedures that you are supposed to be following. For example, when departing a field at night, even if VFR, I will tend to follow the instrument departure procedures.
Your last one is perhaps an example of using the technology as a crutch. "Denied an IFR departure and have to go VFR." I'm not quite sure when that would happen, since it's never happened to me. At that point you are choosing to take off under a situation that may potentially have degraded safety situations. If you are then using the shiny toys to say "I'm not worried about flying VFR around these mountains at night - after all I have synthetic vision," then I would argue that's an improper use of them. You are then making the shiny tool a required flight component. Synthetic vision is not to be confused with military NVGs. One of my friends flies military contracts going into remote airstrips at night with NVGs, no landing lights (state-side, training). He's received special training and approval for this. Keep in mind, your synthetic vision is not NVGs. It's not SAR radar that can actually paint a picture of terrain up ahead (note: I would not use my RDR-130 or KWX-56 for this - they aren't intended for that).
This is why I said the pilot needs to know how and when to use them, and when not to.
Let's see: VSI's, DG's, AI's, Nav. heads, Loran, radar altimeters, autopilots, HSI's, strikefinders, GPS, XM, electronic charts, SVT, AHRS... none of it increases safety if you just ask the right pilot.
For some pilots, those items don't increase safety. All the features in the world don't increase safety if:
1) You don't know how to use them
2) You use them in manners that are inappropriate
Example: The planes I fly these days have de-ice equipment on them. That makes flying in icing conditions something that I can do legally, and in many cases, safely. That does NOT mean that it's an invitation to go out flying in any kind of icing conditions. To do so would be foolish.
If that's "bright and shiny syndrome", OK.
"Bright and shiny syndrome" has less to do with liking equipment (I like equipment) and more to do with a failure to understand the capabilities and limitations, both legally and practically, of that equipment.