The idea behind that is that recidivism is best prevented by letting people be normal parts of society (=being able to work and live in peace) once they have served their term.
Eventually it just becomes easier to just say "no felons" than to try to figure out whether this particular brand of felony is going to negatively impact you or your other residents.
On the other hand, felons have to live somewhere...
As someone who has worked on tenant screening software, landlords typically care about a criminal history involving sex offenses or drug manufacturing. In case of recidivism, the former creates liability from other tenants if issues arise during tenancy, and the latter has potential for property destruction and/or harm to neighboring units.
There are also typically time limits on how far "back" they can look, typically 5-7 years at the most.