Before abolishing parking meters and charging for parking it's important to work out why we did this in the first place. It's an example of Chesterton's Fence: before you remove the obstacle you need to work out why it was placed there in the first place. Only then can you work out whether the reason is now obsolete, to that the fence is defunct. And the original point of parking meters wasn't to charge people for parking, nor to ration spaces by price, not at all:
Shoppers in small-town high streets should be allowed to park free, a minister has indicated, as figures show that councils are raising more money than ever from motorists. Marcus Jones, who was made high streets minister in David Cameron’s post-election reshuffle, suggested that small town centres could become “parking meter-free zones” in an effort to save shops from closure. The Government is growing increasingly concerned that punitive parking costs and fines are deterring shoppers from using their local high streets.
The original reason for parking meters was to increase the number of people using the area.
If parking is entirely free then some goodly number of people will use it all day and possibly every day. This takes up those scarce parking spaces. So, if you want to increase the number of people that pass through an area you want people to have free parking but only for some limited period of time. Then they will move on and others will be able to use the space to visit the area.
Thus, if your intention is to increase the human traffic through an area like a local High Street the answer is not to have free parking at all. It's to have free parking for some limited period of time. On the order of free for an hour, no return within an hour, those sorts of restrictions, rather than "park here all day for free". All of the parking meters and ticket machines needed are already in place. Just program them to issue the first hour's ticket for free.