Lots of misunderstandings here.
First, there is the total misunderstanding with regard to the difference between VFR - Visual Flight Rules and navigation techniques. They are not the same and in fact are not in any way related. The main requirement on a VFR flight is to remain in VMC. There are some others but how the flight navigates is not one of them. Remember that the requirement for adequate lookout applies to all flights - VFR and IFR and as BEagle correctly pointed out VFR is legal above an overcast provided that it is VMC.
If IO540 can not navigate from A to B across Europe without a GPS that is more an issue with IO540's abilities than a problem with the system of navigation when properly taught.
Ded Reckoning (DR) is not a navigation technique in it's self. DR is simply a method of projecting where one expects the aircraft to be at a future time based on certain assumptions.
VFR flights generally use
Visual Navigation they look out the window and see where they are. At the lower levels this is the most accurate form of navigation.
Pilots using Visual navigation will also often use DR to give a heading to fly and then update this heading based on their actual progress (visual navigation). This is the primary method of navigation taught. DR and other associated methods are also covered. Problem is that at PPL and CPL level the candidate is required to demonstrate the ability to apply DR during the test and unfortunately this is mistaken for a requirement to use DR as a sole technique and at all times. That is not the case.
Let's make some things clear - Sole means of navigation means that the information derived from that source is the only information on which the progress (and safety) of the aircraft is based on.
Primary source of navigation means that more than one source of navigation information is available but should there be a difference in information the primary source will be deemed correct.
Also, for an electronic system to be used as sole or primary source of navigation information it must be an approved instalation and must meet the applicable performance requirements. This applies to unfiltered VOR instalations as much as unapproved GPS instalations. No handheld GPS (or other) units are approved.
So for the average VFR flight unless they have an approved GPS instalation and comply with the requirements for using such an instalation the GPS will never be either the sole source or the primary source of navigational information.
BEagle mentioned flying above an overcast. Yes DR can be used provided that an appropriate allowance is made for the lack of updates from visual navigation and therefore after 100nm the circle within which the aircraft could be may be large if there is a strong wind. Same goes for flying across the ocean. However, while a handheld GPS can in such cases provide some information which is always better than none at all, it would be rather poor technique to set out on a flight above an 8/8 cloud layer without having first determined a DR heading and time i.e. relying on the GPS to provide these.
Therefore one could argue that pilots who can't navigate visually and who only get by using a GPS are permanently lost even when visual with the surface and as everyone knows when lost any information is better than no information al all - eh IO540?
In sumary, not having the ability to navigate accurately without GPS does not in any way mean that Visual Navigaytion is any less efficient or accurate when done by a competent pilot (of any level). Unless the GPS instalation is approved it can not be used as primary or sole source of navigation information.
Finally, GPS does not replace DR. One still has to complete a plan pre-flight which of course will be DR since the actual winds etc are not known at that stage. During flight while GPS will provide a continuous indication of position and track it will only ever display the current track and curent groundspeed. Therefore for efficient navigation the pilot needs to be able to apply DR to future progress inorder to determine what the groundspeed will be on different tracks and also to work out what heading to fly to follow a track of 090 when the current track is 060 and the wind is 180/30.
It has taken a long time for GPS to evolve to the current situation where when you look at the screen it looks very similar to what you see when you look out the window. I still find it hard to understand how an older GPS with very few ground features indicated provides more information than looking out the window where everything is in full view. Oh of course, it is very hard to read the road signs from 2000ft and the GPS names the towns - yes, but isn't the inability to read a map and know what the name of the town over there is the fault of the pilot rather than the system of navigation??