An idea I had for circle management

The games that I enjoy the least are the games in which I'm on the wrong side of the circle, and failing to find some wheels. Not only am I running for 75% of the game, but if I do manage to make my way into the play zone, I'm often under geared and about to die anyways.

An idea I had to help alleviate some of the circle pressure is as follows, let me know what you think;

For every ~3-5 seconds that you are out of the circle, your health bar takes 1 point of 'blue damage'. That translates to about 5-8.5 minutes of 'blue damage' before you actually die.

You don't actually take damage to your health bar, unless it fills, in which case you die to zone damage.

On top of this, to prevent people from strategizing around this, when you take bullet/fall damage, you can no longer heal past the blue damage you have taken.

i.e. You have 100 hit points. But you have been out of the circle for one minute. That gives you 12 points of Blue-Damage, you are then hit with a bullet, and drop to 80 hit points. You drink an energy drink, but it only brings you to 88 hit points.

I'm most frustrated when I'm chugging energy drinks and painkillers and bandaging just to barely make it into play zone for it to move all over again. And I think this is a great way to encourage mobility, while eliminating some of the frustration of travel.

Let me know what your thoughts are!