with reference to CB's origanal OP. If there's 2-4 companies making brass. Plus assuming that the metallurgical properties of the brass can not be too much different. Then from a safety piont of view. A thicker walled case woud be better would it not.
No, quite the opposite.
A thicker walled case will have smaller internal capacity. For the same powder charge the smaller capacity case will generate higher pressure. For some powders a small decrease in case volume can give a pressure "spike" out of all proportion to the percentage reduction in case volume. This is because most powders burn faster as the chamber pressure increases, indeed rifle powders typically contain retardent chemicals or surface coatings to try to reduce this effect, which could otherwise runaway with disastrous results.
A charge that is safe in the larger capacity thin walled case may generate dangerous pressure in the smaller thicker case. The opposite situation is most unlikely to be unsafe.
This is one problem using military brass, e.g. .308 vs 7.62, and .223 vs. 5.56
In the case of .223 vs 5.56 some military 5.56 cases e.g. Radway Green are much much thicker than .223 and excessive pressure could easily be caused if safe .223 loads are not reduced.
In the case of .308 vs. 7.62 its even worse, as .308 is rated for 60,000 psi but 7.62 is only 50,000 psi. If you used a top-end .308 load in a smaller capacity (thicker brass) 7.62 case the pressures could easily rise much higher than 60,000 PSI. The brass could well fail, and if used in a rifle proofed only for 7.62 the rifle itself might be in danger of failure. This has been a concern for Lee Enfield .303s converted to 7.62, indeed ISTR they are banned from Bisley because of safety concerns about people shooting .308 or reloads instead of the lower pressure 7.62 rounds for which they were designed.
If you are relying on the slight extra thickness of a heavier case to somehow give some added safety factor you are deluding yourself. If you are working at pressures anywhere close to the yield strength of the case then you are playing with fire.
Heavier brass does not necessarily mean thicker or stronger, in the place where it matters, usually the case head web, nor is all brass of equal strength, indeed parts of the case are totally reliant on "work hardening" during the manufacturing process to improve their strength. If you completely anneal a case to soft condition throughout it is likely to fail completely with normal loads.
Even if the brass properties were identical, and the heavier cases were in direct linear proportion, the case strength would increase with the square of the linear proportion, whereas the case volume would reduce with the cube. So even if pressure rose linearly with the reduction in case volume, the case strength would not increase as fast. In reality things may be expected to be far worse.