On the topic of NFC: my iPhone ApplePay thing taps so much more reliably than any of my credit or debit cards. Is this because it has its own power supply and doesn’t have to first be powered up by the machine?
Powering up the IC actually doesn't take long, but the processing itself can: Contactless payment transactions (mostly) use asymmetric cryptography, and old one at that too (usually RSA), so simply crunching the numbers takes these fairly underpowered ICs quite some time, even when they include cryptographic coprocessors.
Compare that with (symmetric key based) transit ticket authentication, e.g. for MIFARE DESfire or Japanese Felica cards: These usually use DES or AES, which is lightning fast in comparison.