The dangerous part about implementing payload encryption isn't the cipher; mainstream modern ciphers are quite strong and bear few caveats. What's dangerous about encrypting are the constructions you use to apply ciphers to actual data (the "modes", though this is a terrible term that needs to go away).

Cascading ciphers does nothing to address the dangerous part of encrypting (order of operations for authenticating, authenticating all the security-sensitive components of the message, validating authenticators safely, randomizing encryption, safely handling truncation of authentication tags, providing adequate headroom for nonces, &c &c). In fact, since the best modern authenticated encryption constructions tend to be built up from a single cipher core (usually AES), cascades make encrypting safely harder.

You could "cascade" authenticated constructions, but different constructions have different failure modes. The poly MAC constructions fail and cough up authentication keys. Some gracefully handle truncation and some don't. Some constructions fail somewhat resiliently if nonces get repeated; some explode; some purport not to seriously fail at all. Some of them can reliably be implemented in software on any platform, but the binary field stuff really wants hardware extended carryless multiplication or you get new side channels. These things aren't designed to snap together in cascades and smushing them together doesn't make a lot of design sense.

It's hard to get this stuff right even when you're making the conventional, boring choices. Cascades involve a lot of "not boring" stuff, and the payoff for that not-boringness is arguably homeopathic.