Marx build his theories upon a version of Adam Smith's labor theory of value.Smith's labor theory of value posits that ultimately all value is derived from labor. Following Smith Wealth of Nations Book 1, chapter V:
The real price of every thing, what every thing really costs to the man who wants to acquire it, is the toil and trouble of acquiring it.
that is in Smith's view all value was derived from labor.
Karl Marx in das Kapital took this idea to new level. For Marx, went little bit beyond Smith's labor theory of value (which implied that for two goods having same price they must have an equivalent amount of labor), he argued the two goods must have the same amount of "socially necessary" labor (see discussion in Grant & Brue The History of Economic Thought 7th edition pp 149-192).
Marx then used this to critique capitalism. If all goods and services in a capitalist system are sold at prices that reflect their value (and markets under LTV should gravitate to that), and all value is measured in terms of labor, it should be impossible to have profit without exploitation.
In other words, it seems to me that employers’ taking surplus value is a necessary condition for profit, which is a necessary condition for sustainable business. Therefore there is nothing wrong with taking surplus value. Is my argument sound?
From modern economic perspective your criticism would be more or less sound. Modern economics recognizes importance of incentives, and business owners should be compensated for opportunity cost of used capital and their time, in order to provide them incentive to operate. There is also no surplus value from perspective of modern economics. Factors (i.e. labor/capital) either earn their marginal product or if they earn more it is because they have some sort of market power etc. For example, there might be actually markets where employees get extra rents at an expense of employer even.
Furthermore, you should note that most economist no longer believe in labor theory of value (this theory has been discredited ever since the times of Walras and the so called Marginal Revolution - see discussion in Grant & Brue The History of Economic Thought 7th edition pp 211-272).
During the Marginal Revolution economists discovered value is subjective and depends on marginal utility. If there is no objective value determined solely by labor then talking about exploitation in Marxian sense makes no economic sense anymore.
This does not mean we should not discuss consumption, income and wealth inequality, but the framework we have to adopt is one that deals with this issues in terms of subjective marginal utilities. For example, modern study of inequality would discuss the differences between marginal utility of last dollar consumed by person with higher income vs person with low income.
Lastly, you seem to be trying to phrase things in a moral way, i.e. you say "...there is nothing wrong...". This is moral question not economic one. There might be everything wrong about employer being compensated for their entrepreneurial risk, capital, time and labor depending on your moral values/ideology. What is wrong and right has to be explored by moral philosophers, not economists, for that there is Philosophy.se.
How would a Marxist respond?
Marxism is no longer considered part of mainstream economics precisely because over time it became clear the labor theory of value is simply scientifically wrong (i.e. it cannot explain many phenomena that modern subjective theory of value based on marginalism can), and Marxist theories of exploitation rely on the labor theory of value.
Contemporary Marxist economist would likely respond by trying to either claim that labor theory of value is still valid or by trying to propose theory of exploitation that does not build on traditional Marxist economics. Indeed even as late as 80s there were some attempt to vindicate labor theory of value (e.g. see Hunt 1979), but these are not considered successful by majority of the profession.
There are also more recent theories of exploitation that try to get rid of the labor theory of value altogether such as Hodgson (1980), but I do not think they could be still classified as Marxist economics because they seem to be more close to institutional economics. There were also some attempts to reconcile Marxism and Marginalism (e.g. see Steedman 1995 or Roemer 1982), but these attempts seemed to lead nowhere.
Judging by content of standard economic textbooks both of the above mentioned approaches were unsuccessful. Even welfare, public or inequality economists nowadays do not generally talk about exploitation per se, even if exploitation is mention it is not in a context of extracting surplus value. Classical Marxian notion of surplus labor value is incompatible with modern marginalism.
