So if BTB can be AR/BR start....

Why can’t warzone?

Why should it?

got to give the supressor and carbine a chance to be used

You pretty much get level 2 from clearing the home base in warzone so you only need to play for one levels worth with the pistol (instead of the BR, as both load outs have the assault rifle)
So in order to give the magnum a chance to be relevant and used (not many people would chose to spawn with a magnum over a BR ) they need to maintain the current situation with default magnum spawn.

You can set your loadout to whatever you’d like when the req level comes along.

Yes, I also think Warzone is not heavily reliant on the BR as much as it should be.

/sarcasm