As long term growth is provably not impossible, it therefore follows something in your chain of reasoning is incorrect.
In the ideal free market, profit is precisely equal to the costs of obtaining it. If it exceeds that value, it entices further entries into the market and therefore reduces the cost of whatever is in question. If it is under it, some will leave the market, because better opportunities exist elsewhere. As no market is in fact the ideal free market there are various complications in obtaining this, but an overall decline in profitability can be attributed to markets becoming more efficient and effective over time as the tools and knowledge in operating within them improves and becomes more sophisticated.
An ideal market wherein profitability is zero is one with zero wastage, and is hence the most efficient possible means of distribution. It may result in other, undesired consequences, but it is neither economically unsustainable nor intrinsically undesirable, and alterations from that will, by definition, result in inefficiencies. Sometimes this is viewed as necessary from viewpoints other than an economic one, but that's not the level this discussion's operating on, is it?