Is it due to the PET material that it is made of or is it more the shape and structure of the bottle? If it is due to the shape/structure of the container, is it possible to achieve such pressure resistance using another plastic?
Is it due to the PET material that it is made of or is it more the shape and structure of the bottle?
Short answer: Partially because of both. With that I mean it would be possible to produce weaker bottles changing the material or changing the usual design of the bottles.
If it is due to the shape/structure of the container, is it possible to achieve such pressure resistance using another plastic
Short answer: It is because of both, being impossible to say what contributes more without a definition of contribution to resistance. Yes, it would be possible to use other polymers.
Comment about the material: The resistance to pressure of polymer containers usually depends on the combination of three tensil properties:
- ultimate tensile strength (force needed to break it pulling from extremities);
- tensile elongation (how much you can pull it apart until it rips);
- tensile modulus ( ratio of stress to elastic strain in tension).
The table below illustrates these values for some polymers:
As shown in the table, PET doesn't have the highest values. However, it does withstand reasonable pressure and certainly within the limits of proposed use.
Comment about the shape: Intuitively, if standing the pressure was the only requirement, the ideal shape would be a sphere. Although a sphere would allow thinner walls without deforming, I believe it is not usually chosen because of ergonomics and transportation as others have commented ( I have seen one brand of water that has spherical bottles, but I think it was done for aesthetics). The most common designs just prioritise a shape that is easy to hold and without sharp edges.
Why PET was chosen even though it is not the most resistant polymer
Although many other polymers could satisfy the pressure requirement, I believe the reason of why polyethylene terephthalate (PET, material of most soda bottles) is of widespread use is compatibility. Even though PET is what we see everyday, polypropylene (PP), Ethylene-Vinyl Alcohol Copolymer (EVOH), Polyethylene Terephthalate (PET), and other plant derived plastics are used for containers 1. Although I did not do extensive research on their applications, I believe come of blends do satisfy the pressure requirements of 200~700 KiloPascals inside a PET bottle 2.
( The comments below are my personal justification on the compatibility argument)
- Machinery The process of producing machinery for polymer molding usually is polymer specific, that is, not always a machine that molds one polymer can mold another and therefore it is cheaper for industry as a hole to adopt a convention.
- Regulation To test and approve a polymer that stays in long and close contact to food is extremely expensive. Also, considering that the approval must happen for the health agency of every country where the product is sold, there is no reason to make a change for another polymer if you know one that attends your health requirements and that has been tested for decades. I believe one evidence for this is that most os the polymers that I cited are used for bottles of liquids (sometimes pressurised) but not for human consumption.
- Recycling Just as for producing, recycling processes are usually polymer specific, for what they needed to be separated. I don't believe they thought of that by the time the industry adopted the PET as the standard for carbonated drinks, but today it is an extra reason.
I believe that because of these reasons and others (please suggest edits) the transition of PET to anything will take a long time and would be very bothersome. For example, we still were not able to transition completely from glass. In many countries glass is still used for carbonated drinks. This transition was proposed because PET is lighter, doesn't break, cheaper, resistant to microrganisms (which is not so good today as it takes a long time to degrade in nature) and I believe because it was developed in a time when it was believed that men were unable to consume all petroleum available on Earth. However PET is no perfect polymer, it can't for example hold bear for very long, since it has considerable permeability to oxygen. Below there is a table with some permeability data of common use polymers  (unfortunately it doesn't include the other polymers that I said can be used for bottles, but you can find the values online; note that the permeability depends on the gas)
At the moment what is being done is research on different blends of PET that can fill the gaps. In the future, however, there might be a new polymer that takes its place, hopefully addressing the environmental concerns.