Same in C#, but why not have an immutable byte array for bytes and a string for char/runes? Honestly never needed an immutable byte array that wasn't for chars.
Go doesn't have the concept of an immutable array/slice. It's been proposed (largely to bridge the divide between string and []byte), but it doesn't fit quite right with the rest of the language.
Conversely, I could say why not use bytes for both, and that when I need an index lookup it's usually a byte offset. But I think neither statement is totally satisfying, and the more interesting question is why different languages settled on different encodings for strings in RAM.
Microsoft had reasons to pick UTF-16 for C# and the CLR. The Windows API speaks UTF-16, and when C# was first announced way back in 2000, UTF-8 was not yet a widely used encoding on the Web; Unicode was sadly not that widely used on the Web, period. The decision to use 16-bit Unicode in the Win32 API went even further back, to the development leading up to NT 3.1's release in July 1993. At that point, UTF-8 was a relative baby; it was presented at USENIX in January 1993. Also, back then, code points basically were 16 bits because surrogate pairs were but a twinkle in the Unicode Consortium's eye. The Unicode 2.0 standard added surrogate pairs to help them expand their CJK selection and generally let them add more chars of all sorts; it wasn't released until 1996. Now here we are and we have 😃, U+1F603.
Go came along in 2009; by then, many Web sites were being served in UTF-8, and Go'd be used in significant part in Web operations, and UTF-8 was also the default encoding in many Unix environments. Go initially didn't run on Windows at all and was ported by the community, so fitting in with Win32 wasn't an issue. Code points that wouldn't fit in 16 bits were a fact of life by '09, too. Arguments about inherent merits of encodings aside, it probably would have seemed to lots of folks that UTF-8 was a natural choice for that task at that time.
Also, Pike and Thompson are two of the three co-designers of Go and co-designed UTF-8, and UTF-8 was the encoding used by the Plan 9 OS/environment they built at Bell Labs, so, again, technical details aside, it was kind of a foregone conclusion which encoding they'd build the language around. :)
The one thing I do not want to do here is get in an argument about the inherent merits of character encodings, so I'm just not gonna do that. :)
