This is a naive question from a fellow economist.
The model of perfect competition among firms is supposed to eliminate economic profits (a.k.a producers' surplus) in the long run. The idea is that such surplus will bring in new firms, pushing the economic surplus down to nothing, so that there are only normal market rates of return on all factor inputs, explicit and implicit.
Why then does this same model not apply to consumers? I have never seen it stated in any econ text that the entry of new consumers will push their surplus down to zero, including their search costs. Is this a serious inconsistency, or is unlimited entry of new consumers simply not a good way to model most markets? (I suspect the latter.) Even if this is so, should not this asymmetry in our most basic model be explicitly noted?
Yes, economic theory traditionally has emphasized the role of the entry and exit of firms in dividing market surplus. In microeconomics, free entry and exit of firms is an important part of the assumption of free competition. For macroeconomists, modeling entry and exit of firms is important because it is directly related to the creation or destruction of jobs.
Economists usually don't use the words entry and exit for consumers/workers, although they, like firms, also make entry and exit decisions related to their market activity, and their decisions are indeed important for determining what fraction of the total surplus they get.
Consider, for example, an individual market for a given good. Suppose there is a single seller in this market with a fixed supply of the good. Suppose all individual consumer have a demand for an equal one unit of the good. Then depending on how many consumers would enter the market, the market price of the good will imply a larger or smaller share of the total surplus for the consumer. Imagine new consumers keep entering the market, then eventually the surplus for them will go down to zero and no new consumers will enter the market. And, imagine consumers differ in their values outside the market, then while some consumers are entering the market, others may decide to exit it.
In macroeconomics, the worker's decisions on labor market participation is an important part of the model of the labor market.