How to produce “human readable” strings to represent a TimeSpan

To get rid of the complex if and switch constructs you can use a Dictionary lookup for the correct format string based on TotalSeconds and a CustomFormatter to format the supplied Timespan accordingly.

public string GetReadableTimespan(TimeSpan ts)
{
     // formats and its cutoffs based on totalseconds
     var cutoff = new SortedList<long, string> { 
       {59, "{3:S}" }, 
       {60, "{2:M}" },
       {60*60-1, "{2:M}, {3:S}"},
       {60*60, "{1:H}"},
       {24*60*60-1, "{1:H}, {2:M}"},
       {24*60*60, "{0:D}"},
       {Int64.MaxValue , "{0:D}, {1:H}"}
     };

     // find nearest best match
     var find = cutoff.Keys.ToList()
                   .BinarySearch((long)ts.TotalSeconds);
     // negative values indicate a nearest match
     var near = find<0?Math.Abs(find)-1:find;
     // use custom formatter to get the string
     return String.Format(
         new HMSFormatter(), 
         cutoff[cutoff.Keys[near]], 
         ts.Days, 
         ts.Hours, 
         ts.Minutes, 
         ts.Seconds);
}

// formatter for forms of
// seconds/hours/day
public class HMSFormatter:ICustomFormatter, IFormatProvider
{
    // list of Formats, with a P customformat for pluralization
    static Dictionary<string, string> timeformats = new Dictionary<string, string> {
        {"S", "{0:P:Seconds:Second}"},
        {"M", "{0:P:Minutes:Minute}"},
        {"H","{0:P:Hours:Hour}"},
        {"D", "{0:P:Days:Day}"}
    };

    public string Format(string format, object arg, IFormatProvider formatProvider)
    {
        return String.Format(new PluralFormatter(),timeformats[format], arg);
    }

    public object GetFormat(Type formatType)
    {
        return formatType == typeof(ICustomFormatter)?this:null;
    }   
}

// formats a numeric value based on a format P:Plural:Singular
public class PluralFormatter:ICustomFormatter, IFormatProvider
{

   public string Format(string format, object arg, IFormatProvider formatProvider)
   {
     if (arg !=null)
     {
         var parts = format.Split(':'); // ["P", "Plural", "Singular"]

         if (parts[0] == "P") // correct format?
         {
            // which index postion to use
            int partIndex = (arg.ToString() == "1")?2:1;
            // pick string (safe guard for array bounds) and format
            return String.Format("{0} {1}", arg, (parts.Length>partIndex?parts[partIndex]:""));               
         }
     }
     return String.Format(format, arg);
   }

   public object GetFormat(Type formatType)
   {
       return formatType == typeof(ICustomFormatter)?this:null;
   }   
}