What wild places are we talking about here? Surely not the amiable bumps of the Lakes, modified and tamed by men for centuries?
No one is arguing to build a motorway to an Alaskan wilderness or a deep jungle so that what are deemed unworthy types can get there without suffering for days. Actual wild places ought to be kept out of bounds for conservation purposes, particularly from those muppets who can't help poking their nose in every corner of the world for "adventure"...
Easier access is for areas with a well develloped infrastructure, to which you tag on top the necessary add-ons so that people less fortunate than you can also enjoy a nice view or landscape for themselves. Nature is for everybody, not only hikers who want to fantasise the tame little hills they walk on in the UK (and indeed in many other countries) are some fearsome wilderness they are conquering....
However, here lies the problem, easier access means increased pressure on the eco-system. That's why before making it easier for more people to rightfully access their national parks, a proper study of our impact on the landscape should be conducted and then possible solutions implemented.
Probably the best step forward for our national parks would be to ban private traffic within (for non-residents) and install a network of buses from a variety of big P&R car parks at the boundaries taking people to most areas.You could even include a number of limited access areas so that only fit, righteous hikers can get to them and be spared the sight of unworthy visitors...I can only imagine this would be enthusiastically greeted by the outdoors community, imagine the fun on those buses... 
Enforced closure of hills on a rotating basis would be a good idea too, one year it's Helvellyn out of bound, the next Scafell, etc. Give the landscape a chance to regenerate and maybe force people to discover other less popular hills...It would add a good thrill for the more "extreme" hikers to trespass and "wildcamp" in the banned areas. Imagine what fun it would be to blog and tweet about that from the, ahem, wilds...