I can't think of many 'front line bowlers' who have been good or great captains.
Illy was a good captain but you wouldn't call him a front line bowler.
The odd keeper/batsman has done well but in general all the best captains have been batsmen. Mind you, all the best or at least most successful captains have had very good to great teams behind them.
A captain who is a front line bowler may not take himself off at the right time for a start.
All of the above England captains you mention TD with the exception of Vaughan had pretty crap teams playing against some very good teams for most of their tenure.