But it would break compatibility for anyone that's using http.ServeContent as a function value.

To do what you want, you could wrap the ResponseWriter with one that records errors etc. I know this isn't ideal.

No, I can't wrap cause I still could not access bytes copied (and it is primary reason for issue).

At the moment, I see that it looks like I ought to copy whole ServeContent implementation to achieve goal.

may be there is possibility to make checkETag and checkLastModified public?
or make serveContent to be a public function with different name, like DoServeContent(...)(int64, error)?

You can wrap both the io.ReadSeeker and the http.ResponseWriter with something that counts the bytes copied:

package main

import (
        "io"
        "log"
        "net/http"
        "strings"
        "time"
)

func main() {
        http.HandleFunc("/", handler)
        log.Fatal(http.ListenAndServe("localhost:8080", nil))
}

func handler(rw http.ResponseWriter, r *http.Request) {
        rs := strings.NewReader("content")
        crs := &countingReadSeeker{ReadSeeker: rs}
        crw := &countingResponseWriter{ResponseWriter: rw}
        http.ServeContent(crw, r, "file.txt", time.Now(), crs)
        log.Printf("read %v bytes, wrote %v bytes", crs.count, crw.count)
}

type countingReadSeeker struct {
        io.ReadSeeker
        count int64
}

func (r *countingReadSeeker) Read(b []byte) (n int, err error) {
        n, err = r.ReadSeeker.Read(b)
        r.count += int64(n)
        return
}

type countingResponseWriter struct {
        http.ResponseWriter
        count int64
}

Yes, we can't change the signature of things due to the Go 1 API compatibility promise.

But you can expose new function: just make private function 'serveContent' to be a public one with non colliding name, and make it return bytes and error.
For example, it could be named as "ServeContentImpl", "ServeContentInternal" or other.

ServeContent hasn't changed in years. If you want to access its internals, just make a copy.

And now I do not offer to change ServeContent, i offer to make serveContent public with changed name and return type.

Your minor convenience isn't worth the cost of all other Go programmer's increased cognitive load required by having more stuff in the net/http package to read and understand the difference between.

Sorry, we're not adding this. There are ways to do this already. Unless a large number/percentage of people needed this, it's not worth the cost of adding it.