Different statistical tests answer different questions. The $t$ test comes in many flavours, but the most simple one answers the question whether the mean of a population is different from zero¹. The sign test answers the slightly different question whether the median of a population is different from zero. The Kolmogorov–Smirnov test answers the question whether two populations differ. Tests also differ in their requirements on the data, but this can be considered a detail of the question they answer. (The $t$ test also has its requirements that are however not relevant to this question.)
When teaching the concepts of hypothesis tests, I (and probably many others) focus on the $t$ test and sign test, because they answer the arguably most simple question a statistical test can answer. As the students usually have enough trouble wrapping their mind around the concept of statistical testing, I do not want them to additionally burden them with understanding a more complicated scenario, such as investigating correlations. On top, the mathematical backbone of these tests are easy to grasp for those audiences who can appreciate them.
However, the $t$ test answering a simple question does not make it a bad test that should never be used. If you have the corresponding question on your data, it may be exactly the right tool. Note that the fact the statistical question posed by your academic research is simple doesn’t mean that your entire research is simple. There is a lot of sophisticated academic research that correctly employs the $t$ test.
Of course, researchers should make sure that they really need the answer that the $t$ test provides, in particular ensuring that its requirements are fulfilled, and sadly they often fail at this. But that’s a problem with every statistical test – it has nothing to do with the $t$ test answering a simple question.
So, the student’s statement is roughly as wrong as the following:
Addition is the most fundamental arithmetic operation and only a beginner’s exercise in mathematics. Nobody in academia uses it nowadays.
¹ or more precisely: If I sample from a population with zero mean and certain other properties, how likely is it that the mean of the samples is as extreme as that of the given sample?