Having seen language in digital contract signing that basically say that you have to agree to use an e-signature as a signature, I feel like there's a bit of a problem in that needing to agree to use an e-signature suffers the same problem as needing to agree to use an e-signature, in that you sort of should, if you have to agree to digital signing, have an ever-backwards-stretching line of agreements that need to be agreed to...but this is obviously not how it works in practice, so how is it actually working?
Every state except New York, Illinois, and Washington has adopted the Uniform Electronic Transactions Act, and those three states have adopted their own electronic signature laws. At the federal level, a law known as ESIGN provides that electronic signatures are valid, and preempts state laws unless the state has adopted UETA or has its own electronic signature law compatible with ESIGN.
One requirement of UETA is that both parties have to agree to use electronic signatures. It can't be forced on a party. If you send me a contract electronically and I electronically sign it, the question is whether I meant "I agree to be bound" or something else (like "I read it, this looks fine, send over a paper copy to sign"). By putting in the agreement "I agree to use an e-signature," it's hard to argue that you didn't mean to accept the contract. If you didn't mean to use your e-signature to accept, you shouldn't have put it on a contract saying "an e-signature is accepting the contract."
However, you don't necessarily need to put that in the contract for the e-signature to be valid. The question is the intent of the parties, and the court can look at all relevant evidence to decide whether both sides really meant to use e-signatures to accept the contract.
Contract validity does not depend on a signature at all, regardless of its type. Signatures are just a good way of showing that a given party agrees to the terms of a contract recorded by a given document, that shortcut the need for an independent third party to verify any and all contracts.
An agreement can be implied or explicit that the parties consider a digital signature to be an acceptable option, and use that to complete an agreement that the parties consider a digital signature to be the only acceptable option.