After a recent lunch at a local diner, the waiter returned my credit card with an apology: The card-processing system was down. A moment of panic ensued; neither I nor my daughter was carrying cash.

"No problem," the waiter assured us, they could write down my card particulars (number, expiry date, CVV number) to be manually entered later, when their system was back online. Having your credit card information floating around for all to see isn't ideal from a security standpoint. But there was no drama, no crisis. What there was was a reminder of just how little the use of cash figures into my daily life.

And I'm hardly alone in carrying a cash-free wallet. For better or worse, we're headed for a cashless world, where most payments are made with credit cards rather than an exchange of bills or coins.....

In some ways, that's a good thing, not least because using a credit card can be very rewarding. Earning frequent flyer miles or cash rebates has become an expected part of paying with plastic, as card issuers compete ever more fiercely for customers. For some consumers, maximizing credit-card rewards has become a practice pursued with almost religious fervor.

But when it comes to using a credit card, many of the largest payments are off the table. Financial institutions, for example, generally don't accept credit cards for mortgage payments. (Except when they do.) The IRS and state governments don't accept credit-card payments for taxes. College and university tuition, the same.

There is a workaround, however. Plastiq.com is an online service that allows consumers to use their credit cards to pay rent, make mortgage payments, pay taxes and school tuition, and make other payments with organizations that don't normally accept credit cards. Naturally there's a fee to pay through Plastiq: 2.5 percent of the payment amount.

Plastiq's sales pitch is that the credit card rewards—frequent flyer points or cash rebates—are worth more than the fee to use their service, so consumers are ahead of the game even after ponying up the fee. That can be true, but with most credit-card rewards amounting to a rebate of between 1 and 2 percent, that 2.5 percent hurdle is hard to overcome.

There are ways to reliably exceed that 2.5 percent return-on-investment threshold, however, or to lower the threshold. The first is to take advantage of the award discounts fairly routinely offered by airline and hotel programs. When an award requires fewer points, those points are effectively worth more, and are more likely to generate an effective rebate in excess of 2.5 percent.

The other way to make Plastiq a financially rational choice is to take advantage of Plastiq's own promotions. For example, in March, the company waived the fee for the first two rent or mortgage payments for customers willing to commit to a series of six scheduled payments. That would effectively lower the fee for the six payments from 2.5 to 1.7 percent.

One scenario where using Plastiq even with its 2.5 percent fee might be justifiable is in meeting the spend requirement to earn an outsized sign-up bonus for a new card. Over the past few years, many credit-card issuers have offered new cardholders lucrative sign-up bonuses of as much as 100,000 points, typically after spending $3,000 during the first three months. With such rich rewards in play, it might well be worth making some payments through Plastiq to trigger the bonus payout.

So yes, there are situations where paying with Plastiq is a sensible option. But they're few and far between. Which suggests that the service should come bundled with the following caveat: Just because you can, doesn't mean you should.