There is actually a difference in expected outcomes at lottery if you choose different numbers. Commonly played number will be shared among all winners, so your share will be less than with rare numbers.
The less used numbers still have a negative expected value, but you are correct in that numbers 1-12 and 13-31 do have lower payouts because people commonly bet on dates like birthdays.
The problem with this is it presupposes you have some actual chance of winning. You don't, no one splits $0.