One interesting thing about LLMs is that they can actually recover (and without error loops). You can have a step that doesn't work right, and a later step can use its common-sense knowledge to ignore some of the missing results, conflicting information, etc. One of the problems with developing with LLMs is that the machine will often cover up bugs! You think it's giving sub-par results but actually you've given it conflicting or incomplete instructions.
Another opportunity is that you can have less steps or more shared context. One interesting thing about Whisper is that it's not just straight speech recognition but can also be prompted and given context to understand what sort of thing the speech may be about, increasing its accuracy considerably. LLM Vision models also do this with things like OCR. This might not help it with the individual digits in an account number, but it does help with distinguishing an account number from a street address on a check.
Or to take another old-style ML technique, you probably shouldn't be doing sentiment analysis in some pipeline, because you don't need to: instead you should step back and look at the purpose of the sentiment analysis and see if you can connect that purpose directly with the original text.
All that said, you definitely can write pipelines with compounding errors. We haven't collectively learned how to factor problems and engineer these systems with LLMs yet. Among the things I think we have to do is connect the tools more directly with user intention (effectively flatting another error-inducing part of the pipeline), and make the pipelines collaborative with users. This is more complex and distinctly not autonomous, but then hopefully you are addressing a broader problem or doing so in a more complete way.