Replace Cisco, and Akamai and then maybe I'll be convinced it's better than the current situation. But it's still oxymoronic service: A central authority that *REQUIRES* trust for people who don't trust anybody.
First, if you don't trust Cisco and Akamai to that extent, how do you intend to avoid transporting any of your data on networks that use any of their hardware or software?
Second, I think a lot of people really have no idea how SSL/TLS actually work. There's two forms of trust involved with SSL certificate authorities. The first involves the server operators. Server ops have to trust that CAs behave reasonably when it comes to protecting the process of acquiring certs in a domain name. But that trust has nothing to do with actually using the service. Whether you use a CA or not, you have to trust that *all* trusted CAs behave accordingly. If Let's Encrypt, or Godaddy, or Network Solutions, is compromised or acts maliciously they can generate domain certs that masquerade as you whether you use them or not. As a web server operator if you don't trust Let's Encrypt, not using their service does nothing to improve the situation, because they can issue certs on your behalf whether you use them or not - so can Mozilla, so can Microsoft, so can Godaddy.
The real trust is actually on the end user side: they, or rather their browsers, trust CAs based on which signing certs they have in their repositories. Its really end users that have to decide if they trust a server and server identity or not, and the SSL cert system is designed to assist them, not server operators, to make a reasonable decision. If you, as an end user decide not to trust Let's Encrypt, you can revoke their cert from your browser. Then your browser will no longer trust Let's Encrypt certs and generate browser warnings when communicating with any site using them, and you as the end user can then decide what to do next, including deciding not to connect to them.
Seeing as how the point of the service is to improve the adoption of TLS for sites that don't currently use it, refusing to trust a Let's Encrypt protected website that was going pure cleartext last week seems totally nonsensical to me, unless you also don't trust HTTP sites as well and refuse to connect to anything that doesn't support HTTPS.
Lastly, if you literally don't trust anybody, I don't know how you could even use the internet in any form in the first place. You have to place a certain level of trust in the equipment manufacturers, the software writers, the transport networks. If all of them acted maliciously, you can't trust anything you send or do.
I don't necessarily trust the Let's Encrypt people enough to believe they will operate the system perfectly, and I don't believe they are absolutely immune from compromise. But I do think the motives of people adding encryption to things currently not encrypted at all is likely to be reasonable, because no malicious actor would be trying to make it easier to encrypt sites that have lagged and would otherwise continue to lag behind adopting any protection at all. Even if they are capable of compromising the system, that is quixotic at best. Even in the best case scenario they would be making things a lot harder for themselves, and in the long run getting people accustomed to using encryption with a system like this can only accelerate the adoption of even stronger encryption down the road.