Significance tests are used for a variety of reasons and in many research scenarios. One of them is checking the equality of sample sizes.
There’s a book for psychologists whose authors recommend chi-squared test to check if two samples are of the same size. First sample size is 50 and the other one is 53. Then they use chi-squared test to find out if 50 is statistically equal to 53. If it is, then a researcher can state equal sample sizes (f.e. for t-tests or ANOVA, etc).
Q: Isn’t it a really bad way to use significance tests?
It does not look like good advice, but not knowing the authors’ intention what to say? But, more important, it is not needed. Anova or t-tests with unequal sample sizes is not a problem (it might be inefficient, so in the planning phase try to avoid it.)
See for instance Are unequal groups a problem for one-way ANOVA? and many similar posts you can find by searching this site!