It's easier to create many disposable email addresses than "real" email. To get a new "real" email address, you need to fill a lengthy form (e.g., try it on Gmail.com now) and it's not easy to automate the process. But it takes only one-click to create a new disposable email address. Some disposable email providers also provide APIs, so you can create addresses in batch.

People may exploit paid services by creating many new accounts -

1. Free trials: When trail period ends, create a new account.

2. Services with metered billing: Use the service, then refuse to pay. Then create a new account. Then refuse to pay. Then create a new account...

Of course, (theoretically) if the service provider has enough resources (i.e., money, time, knowledge...), they can always find a better solution than banning all disposable emails.