Suppose you had four strikes to strike out in baseball instead of three? That would make pitching much more difficulty by reducing the number of strike-outs. Or four outs in an inning rather than 3? That would tip the balance toward offense.
In football, you have four chances to make another first down. But the last chance is virtually worthless, most of the time, because teams typically kick it away to the other team. So a team that never punted would have four chances instead of three. That is in increase of 33.33333333%! Put another way, on third down, you would now have two chances, or double the chance, of making a first down. More than double, in fact, since the third down would get you a bit closer to the first line goal. So teams punt because of football convention, not because it is a good idea, most of the time. It is about minimizing harm rather than maximizing benefit, since, if you don't make it on 4th down, then you are giving the other team better field position.
I can see some places you should punt: when you are deep in your own territory and you would be giving them an automatic score, etc... Or at certain positions in the game clock, or if conditions are just right. But just punting every single time on fourth down is rather pointless.
I hate sports analogies, but think about this for a minute next time you are in a position to "punt."
Punting can feel like a defeat, but there are other times you have to let go of something and pull back, put less effort into something. Punting in this sense is good thing.