Apple Pay

ApplePay is a service between you, your card issuer(s), and the payments system infrastructure.

If you have no cards registered in your wallet, you don’t “have it.”

Wallet can optionally remain as it’s an integral component of iOS; even if empty. (not unlike how “Notes” remains even if you don’t use it or have any actual notes)

Wallet app can even be deleted on your iPhone. The app can be downloaded again, from Apple App Store. So, if you’re not going to use Wallet app for tickets, boarding passes loyalty cards etc., just delete.