Unfortunately, the console.log() method will only write out a string to a single line and doesn't support the appending behavior you are looking for.

As you detailed in your original post, you could accomplish writing the final result out through the use of a variable (i.e. displaying the final concatenated string), but not continually appending to the same line within the console itself as the loop is being iterated over.

Alternative Grouping Option

The concept of grouping entries is supported, which is obviously very different than your original ask, but it may be worth considering as mentioned in the documentation for console.group() and might look something like this:

var rollingConcatenation = '';
console.group("Looping Group Example");
for (let i = 0; i<=9;i++){
     rollingConcatenation += i;
     console.log(rollingConcatenation);    
}
console.groupEnd();

This can give your console the following appearance, which can help with readability (depending on your use cases):

Do It Yourself Implementation

Another option might be to store your current console value within a variable and at clear it and rewrite the updated values out. Depending on your very specific use cases, you could achieve the behavior you are looking for using something like this crude implementation:

// Define a custom console
var customConsole = {
  // Store a reference to your backing value
  tempValue: '',
  // Always write out the most recent value
  log: function(msg) {
    this.tempValue += msg;
    console.clear();
    console.log(this.tempValue);
  },
  // A clear method to clear the backing console
  clear: function() {
    this.tempValue = '';
    console.clear();
  }
}

for (var i = 0; i < 10; i++) {
  // Use your custom console instead of the normal one
  customConsole.log(i);
}

Take a new variable outside the loop and then prepare that string inside the loop and then you can console.log() outside the loop.

var str = '';
for (let i = 0; i <= 9; i++) {
  str += i;
}
console.log(str);