Bristol, in common with many other Councils, were charged with addressing these issues. The way they did it (which in the case of Barton Hill/ St Phillips was to put up high rise blocks of flats for some, and move the rest to such places as Stockwood and Hartcliffe) could be argued against with the benefit of hindsight (a bit like the Beeching closure programme) but, at the time, it was seen as the modern way ahead.
I too know the issues of the time, but I think the powers that be overlooked - or had no inkling, of the social impact the mass re-locations had. For many years, I lived on Stapleton Road and worked the local bars, particularly around St Judes (The Swan with Two Necks, The Waggon & Horses etc). Unbelievably, 70 years on after St Judes was cleared, people would still return from places like Hartcliffe on a Saturday night for the regular "knees up" or for a Sunday lunch time drink. Despite being children when they were moved out, they still had strong ties to the area and to their former neighbours, as did their parents. Even their own children and grand children still came, suggesting it was an inter-generational thing, though I admit it seems to be finally dying out over these last ten years.
I have heard many stories of people feeling totally "lost" in the wildernesses of Hartcliffe, Southmead and the other estates. No amenities, in some cases little better than mud roads, unknown neighbours - but a decent house, with a garden and a tempramental Ascot water heater at best! And no pub on the street corner ... plus a new, long and expensive bus ride to work or to the shops.
Alas, it is easy to look back with rose-tinted glasses at where we have come from and times were, of course, far harder than they are now. It might have been done to alleviate chronic overcrowding and insanitary conditions (generally down to lack of investment and greed by money grabbing private landlords, featuring prominently the church), but I believe the 1930s-60s slum clearances were done with several major failings:
1. The alternative "tower block" was no way to live, especially with a family. It was viewed as "cheap, compartmentalized living" for the working classes and as a housing solution, it utterly failed and still does. That's why they're being knocked down ...
2. The re-housing was done almost as a military operation, without consideration of the undoubtedly strong social fabric that was being torn apart.
3. And the one I believe to be the biggest failure, particularly in Bristol, was the planners' vision of the future where the private car was to reign supreme above all. Huge swathes of the city and its older housing demolished purely for road schemes, as the planners revelled in the idea that everyone would have a car and they would be free to sweep through the city unimpeded by any obstruction, such as pedestrians or streets with shops and houses (see Lawrence Hill Roundabout, Easton Way, the M32 for example).
I too had an aunt in the area; she lived in Lincoln Street, backing onto the GWR line. The house was freezing cold, riddled with damp, full of structural defects, and she was as happy as Larry when they pulled it down and put her in a flat in Eccleston House
No doubt she was

But how did she feel ten years, twenty tears on? Back in the 1990s, the Council ran a programme called "Neighborhood Renewal" in Easton. It did an awful lot for the old Victorian houses that escaped the destruction of the 1930s - 60s, just showing that there was an alternative to the clearance programmes - and a viable one too. My enduring belief is that mass clearance was a two-pronged political agenda, driven by the obsession of sweeping away everything old and the desire for a space aged style city infested with zooming private cars.
Maybe that was desirable from their perspective back then - but to me it will always be a short-sighted, destructive mistake. Both in architectural and social terms.