It's not "Disney" who is handling groups in different ways, it is the travel agents that the groups use. Some are more aware than others about the FP+ booking guidelines. Or, I should say, whether they are aware of them or not, some ensure their clients have the information in time to meet the FP+ booking windows, and others don't.
My company, and I know others, understand how important this is to our clients, so we obtain the tickets early enough to provide the numbers to our clients. We can't do ANYTHING about the MB/ticket disconnect for our onsite groups - THAT is Disney's current limitation within their system.
Having said that, there are times that the group might not provide the information they need to book everything to the agent in a timely manner. And that may be the issue with some sports teams, as you mention. The agent can't buy tickets for everyone if they don't know how many tickets to buy!