Log odds preference query

The range of probability values: $[0,1]$, The range of odds values: $[0,\infty]$, The range of log odds values: $[-\infty,+\infty]$

We use log of odds instead of odds and probability in logistic regression as data can be modeled better when values lie in a non-restricted range. What exactly is the issue with values that lie in a restricted range?