I enjoy a good dose of nostalgia and love flying classic taildraggers and - to be honest - nearly anything else in the GA world. Maybe it's a function of my location on the planet but I'm surprised that few posters have mentioned training in the VLA/LSA environment. Many of the aeroplanes available are actually much more interesting to fly than the standard (increasingly clapped-out) traditional GA offerings and, despite the naysayers, we now have professional flying schools offering both GA and Recreational Aviation Australia training, often by the same instructors.
It's true that the originally-mooted cost benefits of this type of flying/training have not all been realized but the cost reduction that has been achieved, and the associated fun factor, are definitely contributing to the continuing viability of private aviation.
And you even have the option of some nice taildraggers, if that's the way you want to train (see, e.g.
Tecnam.com - P92 Tail Dragger).
This type of training won't work for everyone in all circumstances but there's no need for excessive hand-wringing, in my view.