Profit is an accounting term after the arrival of money, and it is based on an assumption that money have constant value, which is not true, it is not necessary to support economy activities. Economy is driven by demand, and its root is desire
Of course, if you use time as a unit of value, then your statement is almost true. Exchange happens because each participants could save more time from it. But not everyone is profit-seeking and I guess majority of people are not
I am not a realist: I do not hold "profit" to have an objective existence. "Profit's" existence, for any particular person, is specifically that which it has come to occupy for them. (I will proceed in accordance with this belief.) Profit is a degree whereto one's perception of value - as it is manifest as a response to an exchange - deviates from that of another. Moreover, it is one such degree that is held to be to correspond to one's having secured itself against some calamity.