I think the right thing would be one three-term limit.
Agree. Allowing unlimited terms for the presidency is far more dangerous because it consolidates the entire power of the executive branch in one person allowing for greater chance of abuse and entrenchment that a single senator or congressman. No matter how many terms Byrd or Thurmond serve, as one senator among a hundred they won't accrue a fraction of the power held by the president.
That said, I think allowing the president to potentially serve 12 years instead of 8 demands longer range planning and makes a second term president a more active political entity than a mere lame duck.