I would not support the mandatory use of GPS. It is entirely possible and sensible to navigate accurately using only visual references.
I would support mandatory GPS training as part of the PPL syllabus.
The problem with visual references as the sole means of navigation is that it is a skill that needs to be well taught and regularly practised. The syllabus does not provide sufficient time to teach the skill. I believe this is entirely correct because the syllabus is already long enough. On the other hand there is time within the existing syllabus to introduce to pilots the use and shortcomings of GPS.
A moving map GPS supported by proper training on how to prevent a course being incorrectly entered and executed and supported by visual navigation is almost foolproof and certainly and awful lot more foolproof than anything else available to the average PPL.
Of course it is not perfect and zone infringements will still occur. However in my opinion they would be an awful lot fewer.
GA vitally needs this culture change. GPS is one of the most important pieces of equipment in the cockpit both as a navigational aid but also as a very good means of getting yourself out of trouble. It is also one of the least expensive pieces of kit. I simply have no idea why anyone would want to fly without a moving map GPS even if it was only there as a backup to visual navigation, unless you had complete confidence in your visual navigation in all circumstances (and I accept there are a few who would be able to meet that criteria).