Depends what you consider as ' competing '
Other operators in the market do 'compete' in the letters sector -. just have a look at the envelopes that drops through your letterbox - you'll find a good percentage has a TNT or other , logo on it .
What TNT and other companies do is provide a postal services for business ( which afterall forms the greater percentage of mail sent ) ; where they will collect the mail from the Companies and deposit it into the Royal Mail postal delivery system - paying a fee to Royal Mail to deliver .
The operating cost to TNT thus is far lees that that of Royal Mail .
Added to that they 'cherry pick ' the profitable parts of the business . Afterall which company would want to compete for business , providing a postal service to the hebrides and other loctions ?