So converting floats can sometimes be necessary, and that's what we're talking about. Going via human readable text is only one specific example.
But this has nothing at all to do with floats. If you transmit 16 or 32 bit ints, or any image/video/sound datatype, or even raw bytes, there can be endianness shenanigans. Introducing endianness when talking about floating point numbers is completely offtopic.
So in those cases you need to go through an intermediate representation, and then the question of conversion arises.
So sometimes, when sending a float (as a single example) from one machine to another, you have to go through conversions, and one way to do that is to generate a string representation. The point here and in other comments is that many people think this is easy and obvious, but in truth it's hard and full of pitfalls.
You said:
> I do not understand why would you ever round trip floats through text.
I'm trying to explain that. I have some experience of the issues involved, and was trying to share my experience. You are dismissing it, which is entirely your choice, and in that case, my comments are here for others.
If for you it is an extreme edge case, then I suggest you put it to one side and hope it never becomes relevant. But if one day you find a bug you can't explain, maybe it will help you.
It's part of the reason I developed Concise Encoding: https://github.com/kstenerud/concise-encoding/#example which allows hex float notation when you need to be exact.
If it was just inaccurate! It cannot even deal with straightforward floats like inf, nan, or minus zero!
There are allnkinds of reasons machines talk to each other in human readable formats. APIsare for machine-to-machine communications, and yet APIs that speak JSON or XML are not uncommon.