I see covenants as important here because they're the component of the financial system that's most rigid and non-responsive to changing market conditions. The
point of a covenant is to make a contract more inflexible, by declaring a point beyond which a creditor just won't accept "slack" in the debtor's performance.
If you take covenants out, contracts become inherently more negotiable. And that's important, because frequently creditors have less pressure on them to perform, in exactly the same circumstances that cause debtors to face more challenges; and so creditors often find that their best option, EBITDA-wise, is to eat the losses from the challenges that their debtors are facing, rather than destroying their debtors through liquidation in a way that gets them, in the end, less money.
You know how, right now, corporations are more willing to release previously-withheld "bad news", because they can blame their lack-of-performance on a suspension of work due to the virus? Those corporations are creditors, not just debtors (esp. in commercial paper); and the "slack" they earn like this, they can pass on to their debtors (e.g. other corporations)—but only if contracts work the "normal" way, that you see in small-scale non-covenanted contracts.
In such non-covenanted contracts, where when the regular contract isn't working out, frequently the best thing to do isn't to sue for breach, but rather to just sit down and renegotiate the contract. That's what's going on right now all over the place—contracts between e.g. landlords and renters, or between suppliers and retailers, are being renegotiated, just for this temporary period, to the benefit of both parties. (Another good example, more generally, is personal debt forgiveness: debtors are willing to accept a renegotiation of a loan to an individual, over the much-less-likely chance of ever claiming the full original loan amount.)
With a covenant in place, though, one party has no incentive to sit down to renegotiate (and in fact, that's what they wanted to avoid by adding a covenant); and instead can just pressure the other party to do drastic things like liquidation in order to fulfill the secondary contract stipulations under the covenant-breaking clause.
Wouldn't it make sense to—temporarily!—take away the tool by which funds/banks/institutions force their debtors to liquidate, and instead force them to do the thing they'd have done if that tool wasn't there: to renegotiate performance expectations, to get what return they can get; and then, in turn, have those funds/banks/institutions renegotiate their performance expectations with their creditors?