Thanks, I pushed your patch (with a minor change to make it integrate with the latest grep) and then pushed some fixes and one major simplification: don't have any special case for "grep -iF PAT" when PAT contains no alphabetics. This is rare enough that I expect it's not worth complicating grep to worry about it.

I'm attaching the combined patch, that is the merge of your patch plus my changes.
diff --git a/src/grep.c b/src/grep.c
index 475cb1a..a1bccdb 100644
--- a/src/grep.c
+++ b/src/grep.c
@@ -1904,6 +1904,45 @@ parse_grep_colors (void)
    ? (*(s) = wctob ((wint_t) (wc)), 1) \
    : wcrtomb (s, wc, ps))
 
+/* Change a pattern for fgrep into grep.  */
+static void
+fgrep_to_grep_pattern (size_t len, char const *keys,
+                       size_t *new_len, char **new_keys)
+{
+  char *p = *new_keys = xnmalloc (len + 1, 2);
+  mbstate_t mb_state = { 0 };
+  size_t n;
+
+  for (; len; keys += n, len -= n)
+    {
+      wchar_t wc;
+      n = MBRTOWC (&wc, keys, len, &mb_state);
+      switch (n)
+        {
+        case (size_t) -2:
+          n = len;
+          /* Fall through.  */
+        default:
+          p = mempcpy (p, keys, n);
+          break;
+
+        case (size_t) -1:
+          memset (&mb_state, 0, sizeof mb_state);
+          /* Fall through.  */
+        case 1:
+          *p = '\\';
+          p += strchr ("$*.[\\^", *keys) != NULL;
+          /* Fall through.  */
+        case 0:
+          *p++ = *keys;
+          n = 1;
+          break;
+        }
+    }
+
+  *new_len = p - *new_keys;
+}
+
 /* If the newline-separated regular expressions, KEYS (with length, LEN
    and no trailing NUL byte), are amenable to transformation into
    otherwise equivalent case-ignoring ones, perform the transformation,
@@ -2379,6 +2418,21 @@ main (int argc, char **argv)
   else
     usage (EXIT_TROUBLE);
 
+  /* If case-insensitive fgrep in a multibyte locale, improve
+     performance by using grep instead.  */
+  if (match_icase && compile == Fcompile && MB_CUR_MAX > 1)
+    {
+      size_t new_keycc;
+      char *new_keys;
+      fgrep_to_grep_pattern (keycc, keys, &new_keycc, &new_keys);
+      free (keys);
+      keys = new_keys;
+      keycc = new_keycc;
+      matcher = "grep";
+      compile = Gcompile;
+      execute = EGexecute;
+    }
+
   /* Case-insensitive matching is expensive in multibyte locales
      because a few characters may change size when converted to upper
      or lower case.  To accommodate those, search the input one line

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