Extremely unlikely any of us alive now will be alive to see it. Oil is just far too useful for us to be able to replace easily, and choosing not to replace it would take our lifestyles back hundreds of years. Hardly anyone wants that.
It was used everywhere - as filler, as insulation, as fire retardant, and was so cheap it even got used as bulking agent, as fake snow for Xmas and in packaging. We got rid of it in new applications in just a few years once it was realised that the health cost was far in excess of its utility. It costs thousands to rip out some of the old insulation in buildings, especially where it's part of the fabric of the building.
Lead in petrol was far to useful to be replaced, etc etc...
I just think it's part of the new innovation debt coming due. It's only now coming due for plastics and oil and the extreme cost of profligate unconstrained use is starting to be realised.
It comes from thinking of the planet as infinite and able to absorb anything thrown into it, rather than a closed cycle life support system.
I'm no fan of oil either, but let's not get carried away.
A house need not depend on oil - bricks can still be fired and glass made from carbon neutral electricity, pipes can be copper, and drainage use ceramic like was used until the 80s. Similar for transport, water treatment etc. Perhaps a few specialised uses of PVC and other plastics will remain and the rest go - regulated or priced from existence. Now 95% of coal and horses aren't around we still keep stables for fun, some still enjoy horse racing, steam trains run at weekends and museums run a few steam engines.
Thing is the assumption that the planet could take everything thrown at it used to work - now population has grown so much that no longer applies. JulianMorrison has a point that "it's useful" can no longer be enough - stuff isn't only used by a few wealthy types any more, on a planet with under 1bn, whilst most of those engage in agriculture. We have to learn to consider damage control and restriction far sooner than was necessary even in the 1930s.
My worry is the modern dogma to not want to impact business at all costs. Governments avoid strong regulation, requiring consideration of the land a business occupy, the pollution and waste they cause or the people whose needs they should serve. Essentially they became subservient to multinationals. It will make changing that much harder and fought against much more - not least by those oil interests.
Not easy, but not impossible either. There is precedent after all. :)
The final thing I would say is that if those in control are sincere about tackling climate change, an open borders immigration policy is a very strange thing for them to be promoting. Instead of supporting people to live good lives where they are - in low carbon countries - we are encouraging them to move to high carbon countries, and effectively creating a reason to generate massive amounts of carbon through house building, infrastructure etc. This is one of the main reasons I am sceptical about the messages that come down from on high, and even more so given that the stock response to this issue is accusations of racism etc.
Get rid of plastic forks, spoons, knives, and straws... again no big deal.
Get rid of plastic used in food. Milk jugs, processed food, tv dinners, plastic bags of lemons/potatoes/etc. Kill off water bottles (which are a waste anyways), soda packages in plastic, cheap boxed wine, etc.
Sure there's some harder things, like say fertilizer, car interiors, toys, keyboards, mice, watches, network cables, etc. But still we could hugely reduce are use of oil.
Sadly the world was just starting to move away from oil a bit, then USA went from a large oil importer, to a huge exporter and the prices dropped.