The transformer does not produce or consume current. For the most part, the conductors and OCPD simply need to be sized to the loads.

HOWEVER, you do need to consider the inrush current of a transformer when making your decisions.

Allow me to be a little loose with the math, just to illustrate my point.

Transformer full load amps = 500A

Transformer inrush = 10X FLA

Protective device Instantaneous pick up point = 15X continuous amps.

So your 'primary side' protective device and conductors would need to be a minimum of (500 x 10)/15 = 333.33A, which rounds up to 350A, in order to just turn the transformer on. But if your OCPD had a max Inst. rating of 10X, you would need a 500A device.

How realistic are the 10X inrush and 15X instantaneous trip figures? Do these apply to most transformers, breakers, and fuses across the industry?

Because I've checked your calculation, maintaining the 10X and 15X factors, and it seems like just rounding up to the next standard transformer KVA rating (as you usually have to do) is generally not enough to require any larger OCPD on the grid-side, than you'd already be needing for 125% of the operating current that you'd be using anyway.

1.25/(10/15) = 1.875, and the ratio between adjacent standard KVA ratings is generally between 1.2 and 1.67. There are a couple of exceptions where the ratio is 2, and even then rounding up to the next standard OCPD is enough. So in general, as long as 10X and 15X are typical of the industry, and given the 125% continuous load factor applying by default, I wouldn't expect this calculation to impact a design.

It seems that where you would find this calculation affecting a design, is if you are using a transformer rating that is in excess of simply rounding up to the nearest standard kVA. E.g. you not only round up to 500kVA, you also skip that size, and use 750kVA. I could see specifying this for future expansion, but for that, you'd already be specifying a grid-side circuit for the full capacity you eventually expect. The only other reason I'd see you doing this, is if you were using a reconditioned transformer, and the one that is available is a size larger than you need.