how can bronstein main time fall below the increment? given that you make a move before time expires, shouldn't you have at least the increment time on your clock after making a move?
Let us assume you are playing a game with 5 minutes and 5 seconds per move Bronstein delay. In Bronstein mode your clock starts immediately when your oppenent stops his/her clock. If your main time left is 3 seconds (less than the 5 second delay) you need to make your move in 3 seconds. If you make it in 2 seconds, your clock will go down to 1 second and then delay will be added to your clock and increase time left to 3 seconds. If you do not make your move in 3 seconds you will lose on time. You have to make all of your remaining moves within 3 seconds.
This is much different in simple/US delay. First of all you have 5 seconds before your clock starts. In the Bronstein example you would lose the game if you did not make your move in 3 seconds, whereas here you have 8 (5 seconds delay + 3 seconds on the main time) seconds.
You will have to play your each move within 3 seconds in the Bronstein delay and within 8 seconds in the simple delay for the above example. The main advantage of Bronstein is that you see exactly how much time you have on the clock. Other than this extreme example, both systems are equal.
Also, note that Bronstein delay is equivalent to simple delay (aka US delay).
In that, the clock waits a certain amount (say 3 seconds) each turn, before actually counting down the player's time.
I prefer that because it's easier to explain; the reason Bronstein exists is to easily show players the "total" time they have though.
I think it's easier to explain "when you move you gain X number of seconds"