Those figures are about right for the bare minimum wall thickness for the walls of a cylinder however, as you say, this would be inadequate in practice for a number of reasons.
- Safety concerns dictate that steam pressure vessels are designed with a large factor of safety. You certainly don't want any sort of pressure vessel to be operating anywhere near the yield stress of the material.
- The hoop stress in an ideal cylinder is one thing but the design of the ends (ie lid and base) also have a significant effect on the stresses and pressure on the ends will introduce tensile as well as hoop stresses to the cylinder walls.
- Stress raisers from fittings, catches etc and manufacturing artefacts may cause local stress concentrations well in excess of the calculated figures.
- The pot needs to be robust enough to stand up to everyday use and handling.
- Even when the stresses are at an acceptable level deflections may not be, especially in terms of sealing the lid. To put it another way being strong enough does not guarantee that something is rigid enough.
- Depending on the material, fatigue, work hardening, corrosion embrittlement, thermal stresses, etc etc may be factors.
- From a business perspective it may be preferable to adopt a more conservative design in order to simplify quality control, especially where material costs are a small proportion of overall costs and the risks associated with potential liability or loss of reputation are high.
- A product made from heavier gauge material may be seen as better quality by consumers.
The criterial I have listed are, by their nature, a bit fuzzy. The general approach to this sort of problem is to first do your best estimate based on calculations of the conditions you expect in normal use and then apply a factor of safety. This makes allowances for uncertainty in your calculations, variations in actual material properties and wear and tear over the life of the product as well as unforeseen conditions (to an extent).
In general a larger factor of safety is used where you are less certain about your model either because comprehensive calculations are impractical or conditions of use are difficult to predict. Larger factors of safety are needed when a failure would have safety implications (eg for pressure vessels, lifting equipment etc) but can be mitigated by more rigorous quality control.
It is also worth noting that factors of safety for aerospace are often significantly smaller than for general structures despite the fact that aerospace requires very high levels of reliability and redundancy. The reason for this is that weight/mass savings are so economically important that it is worth spending a lot of resources in the design stage to achieve reliability by testing and very detailed analysis rather than just being generous with loading calculations.
By contrast if you are designing a bridge it usually works out cheaper just to err on the side of caution, especially as you are often choosing between standardised parts, or at least parts fabricated from standard sections rather than designing every single component from scratch.
It is good practice for pressure vessels to be practically proof tested at a pressure in excess of their designed operating pressure. In many cases this is a regulatory requirement.
Finite element analysis software can be a useful tool for optimising designs but it needs to be treated with care and an understanding of its limitations.