Are there any big-endian chips still in production outside the embedded or specialty market?
Even MIPS and PPC now support a little-endian mode and are usually deployed that way. ARM is nearly always LE or deployed that way, and RISC-V is LE.
Edit: bonus factoid:
Little-endian is slightly more confusing for humans but may be objectively better for machines. On a little-endian machine integer size casts are free -- e.g. casting a uint64_t to uint32_t just means reading the first 4 bytes of it. On big-endian machines integer size casts require pointer math.
As way to serialize data (wire / disk format) it's becoming more common. FlatBuffers and Cap'n'Proto are the popular ones. They reduce (completely eliminate?) byte shuffling when de-serializing.
In one instance I was reading a spec for an industry-specific protocol. At first I was looking at it and thinking "What the... they are padding stuff in a strange way, and using little-endian for the data". Then it suddenly dawned on me, that they've designed the spec to be whatever GCC on x86-64 Linux machine would do to layout C the structures in memory.
So someone very lazy could just define a struct and cast into it as data comes from the wire. Someone one a big endian machine, would have to do a lot more legwork to get the thing working. But given that there aren't many of those around, it was deemed an acceptable tradeoff.