If the concern is Let's Encrypt being a SPOF wouldn't a cross-signature from our organization to bootstrap trust in an alternative have the same problem?
Let’s Encrypt could use the ISRG Root X1 certificate to sign other intermediates, but if that root continues to be valid, Let’s Encrypt could also use it to sign new Let’s Encrypt intermediates in case there is a problem with the old ones. So, there might not be a lot of marginal benefit from this course of action.
I’m sure Let’s Encrypt staff would be happy to talk to anyone who wants to set up a new ACME-based CA on the Let’s Encrypt model.
If an alternate CA – say, Lettuce ‘n’ Crypt – were created for redundancy, it would be prudent to stay away from Let’s Encrypt’s software, and design decisions, and even Go, and use a highly independent implementation. ACME can’t really be avoided, but any bugs, outages, or vulnerabilities are likely to be in the ACME protocol, or Let’s Encrypt’s software, or the Go libraries it uses. (Or HTTPS, or Linux, or…)
I doubt this can resolve all of the concerns about the risks created by Let’s Encrypt as a single point of failure, but it’s really nice to see that another CA is now offering a free ACME DV product: the Norwegian CA Buypass.