We do. Here's why: Our management fee is dependent on both owners and tenants abiding by the rules. When tenants pay late, this causes a lot of extra work for us. We must spend time and resources sending notices, listening to their sad stories and complaining, repeating the lease terms, collecting certified funds, spending extra time to deposit the certified funds, and so on. The late fee is our compensation for that extra work.
Furthermore, Late Fees are not a profit center for us. We don't want to deal with late payers' stories and excuses - we would prefer to avoid that disruption entirely. We make every effort to place good tenants who pay their rent. In fact, almost every late payer we've had, was an existing tenant when we took over a rental property, not someone we placed. When tenants pay late, we work hard to collect so we can get owners paid on their correct payment date. The owner never notices the late payment unless the tenant does not pay at all. Bottom line: we do all the work to collect, and it is an extra service, so we keep the late fee.
If this is a dealbreaker for you as an owner, we invite you to find another property manager who will bend more easily. However, we would question how great an advocate they will be for you, when they have to deal with challenging tenants.