Looking at Flybe 2, it is technically possible for them to have no debt. The start-up costs could well have been funded through equity instead of debt but either way, it is money on which either a bank or the shareholder is expecting a fulsome return!
I think other airlines have done exactly as you describe (Eastern for one). Many airlines have taken on loans with Loganair included, and what isn’t clear now is where they all sit. Jet2 reported that they had taken a Government CCFF loan but their cash position was strong and if you look at the net debt position then it was quite strong. Others could well be in the same boat. I think the one thing you can say with certainty is that no airline will have taken on debt just to keep losing money and without taking actions to cut their cash burn radically. No-one is that stupid.
In other words, I don’t think anyone can say for certain whether or not Flybe 2 has a great advantage over others. It might have, but might not.