"in a world of perfect pedestrian infrastructure would more people be likely to walk the sort of distances they currently use a car for?"
Don't really think so.
I live in Inch with almost perfect pedestrian infrastructure, 20mph, generally very little traffic, very few streets suitable for through traffic but many footpaths that connect streets, pavements generally in good condition. I honestly can't think how you could improve the area, except for a cycle path along Gilmerton Rd. and an additional dropped kerb here or there.
Still, many people drive even short distances, I guess 2/3 of local trips are by car, the rest walking. Many of the walkers are children or elderly people who may not be able to drive.
I don't think walking is affected so much by bad/good pedestrian infrastructure.
Car use is high around here because there is plenty of parking, so people have the car right in front of the house and also can easily park at the local shops. It's just the only mode of transport on peoples' minds.
When I lived in a flat nearer the centre, I thought more neighbours walked, even though the pedestrian infrastructure was much worse (cluttered, narrow, damaged pavements, busy roads etc.). Pavements might be unpleasant but normally don't feel unsafe, so most people cope. Some (many elderly) may not go out at all (which is reason enough to improve things), but I don't think perfect pedestrian infrastructure will affect car use much unless driving also becomes inconvenient.
Some more local observations:
Customers at the local shops come from maximal 200 or 300 metres away (anybody further away will go to Sainsbury's or Morrison's), still most drive, or quite frequently a husband drives his wive and waits right in front of the shop with the engine running. These are not shops where you buy bootloads of stuff, but something like a pack of fags or a lottery ticket. Often people drive just down the road to visit relatives or friends.
School traffic at Liberton primary is horrific - ok, the catchment extends quite a bit and Gilmerton Rd is busy at peak times, but most of the pupils must come from within Inch and could walk through purely residential areas or through Inch Park, they may have to cross Gilmerton Rd once. I haven't seen any kids or parents cycling to school, but some kids have bicycles and occasionally ride around the neighbourhood.
Similarly at the Inch Park sports centre, some walk through the park but most drive in and park right in front (I had a big fight for months with the parks management about loads of illegal parking on the grass). The handful of bike racks are always empty. Inch House is the same.
The exception is Bridgend Community Farm where the fence is full of bikes when there is an event on, but the car park is also full, I'd say 1/3 bikes, 1/3 cars, 1/3 walking.
I haven't seen many other local people on bikes, only commuters coming down Gilmerton Rd and some leisure riders on the way to Craigmillar Castle Park.
The shops didn't have bike racks until I nagged council enough to get some installed, and within a week somebody had reversed into them and mangled them up (they've now been moved to a better place but I never see other bikes).
The area would be almost perfect for active travel in terms of distances, infrastructure and public transport, except for some steep roads. Still it's car-dominated.
EDIT: Doesn't mean it's not possible to get modal shift, but I think in the 1950s suburbs like Inch it's not about infrastructure but about "culture" (I know...), changing people's attitudes that the car isn't the only real means of transport.