Does taking the log of odds bring linearity between the odds of the dependent variable & the independent variables by removing skewness in the data? Is this one reason why we use log of odds in logistic regression?
If yes, then is log transformation of data values unnecessary in logistic regression?
It might result in linearity but might not. If you have a true relationship like $\text{logit}\big(\mathbb E[Y\vert X=x]\big) =\beta_0+\beta_1x+\beta_2x^2$, then you have a perfectly valid logistic regression but also need that quadratic term to do the modeling well.
Transforming features ($X$) is a separate issue than the link function. You might find that the relationship between the transformed expected value and the features works much better when you includes something like a quadratic term or a logarithm. However, that’s fairly unrelated to skewness of features and should come down to a combination of domain knowledge and model flexibility (as is the case in linear regression).
In particular, GLMs make no assumptions about features having any particular distribution.
