I'm not sure where you are located but, in the US it's those 3 pieces of information as well. I think checks in the case of validity and legal situations make a lot more sense. Not everyone will have that information at hand, nor do they have banks that are willing to allow them or charge a fee for them. It's also 2 pieces of information more than a cashiers check would require, and discloses where the destination of the funds is going to anyone involved which includes both the handler and the person who is giving you money, where with a cashiers check you can deposit or cash those most anywhere that manages checks, be it your bank, an opposing bank, walmart etc. It also helps with the actual paper trail as you have a physical piece of paper confirming you are going to be receiving the amount, where a wire is fully digital and if something messed up along the way, it can take weeks to resolve the issue. You can't screw a cashiers check up without really trying, it's weighted against the bank itself instead of the person or entity that is owing the money, which means it can't bounce(like normal checks can), and it only needs your name which, the court and the payer should already know, where a wire transfer can be screwed up by a simple typo of the numbers.

The processing speeds are also night and day. You mentioned next day but, that is likely because because your bank is doing you a favor with it. A wire transfer can take up to 5-7 business days to actually transfer, in some cases it can even take up to a couple weeks. Cashier checks are handled similar to government checks and are legally mandated (at least in the US) to be cleared next day. Wire transfers to my knowledge do not have this obligation.