I'm pretty sure I don't agree. Many of the fundamental assumptions in economics aren't just first-order approximations; they're about tractability. You can leave out friction and get reliable ballpark figures, but when you assume monotonicity, you're liable to end up wildly off base sooner or later.
That's what I consider the main problem of economics. To use the gp's expression, they have physics envy when they need to be demanding statistics and psychology. The problem area is difficult and overpopulated, and what's worse, worth money. That means that the most apt people do business for themselves instead of suggesting on the business of others.
Much of economics is useful, but little is reliable. As much as it pains me to say this, I believe we could do with more (quiet) focus on economic policies - just not from the math people, but from the social studies people.
Sure, a number of economists attach undue weight to some underlying assumptions which are only partly true, such as economic actors to some degree exhibiting "economically rational" (perhaps akin to a disciple Newton fan asserting the wave nature of matter has no meaningful implications for their bodies, this kind of abstraction is harmless when applied to sufficiently large numbers). But whilst this economic model appears to break down at levels as simple as individuals being ineffective at computing stochastic optimisations in their heads, it works rather well when analysing the behaviour of crowds. It's not so good at identifying when bubbles will burst, but then meteorologists can't predict the weather next year with any reasonable degree of accuracy either, and that's arguably a simpler system to model.
Where economists overstep the mark is not so much the tendency to oversimplify as the fusion of normative arguments with their models, such as the sleight of hand that dresses Pareto "efficiency" as a static optimisation problem rather than a rights claim made on behalf of the status quo.