I'd like to point out something in S1 you may not have considered, the Jewel Seeds here were on Earth because of a major TSAB mess up. A world apparently in a frontier region of time/space and protected by a non-interferance treaty. Sending the military in the open will not only be tragic because of the rioting monkeys, it's also an admission of error on their part. Also, there may not be suitable agents available to deal with the investigation and blend in at the same time. As it is, a specialist battle group did get sent in S1, not for the Jewel Seed but after Precia herself. Call it answering power with power, otherwise recovering something the TSAB misplaced isn't really high on priority.
Basically the TSAB had no one they could send to Earth to investigate Precia, especially after encountering Fate and her insane speed hax. On the other hand, there was this local wild mage able to chase after the girl, and she was doing it quietly. In light of this, the admiral in charge had 2 choices:
1 Disarm Nanoha because she's a kid with a big gun.
2 Help her with logistics/intel support, training and hide her battles from the locals.
No suprise on the choice.
For sending in the kids to do battle, it may very well be that the children on Mid-child grow up quickly into their power. Not because they are given the training to be able to firebomb a large building on a whim, likely because they ALL can do so from birth. It's the Jedi analogy, imagine having someone able to bend reality as they wish on instinct- now add that to a society where that ability is common place.
What is the government to do in the event a tantrumimg kid or emo teen decides to nuke a shopping mall for fun, unless the discipline is instilled from youth?
My guess is they turned the whole place into a police state and restrict a number of high end artifacts and abilities. Something like the TSAB NO-Fly Zone over the City and a department in charge of hunting down Lost Logia devices. The thing is, the society the TSAB is based on appears to be descended from survivors of previous civilisations with the same problem. It's not pretty but overall IMO the controls they placed on themselves have made them rather stable- despite everyone and their grandma having personal nuclear weapons
.
I doubt these guys can administrate/police the whole range of areas with their manpower. The best possible would be to hold themselves in check, keep what they do in the open for oversight, section off anyone who likely does not have magical abilities in special reservations before hunting down the remnants of lost civilisations.
For S2: Same trouble, Same Place and involving the Same people [Vita hammered Nanoha first]. Having Fate there was probably a genius plan for the book to be completed sooner.
The fact that the highest ranking officer in the TSAB was planning for the book to go wild and explode in his homeworld and out of the TSAB jurisdiction is all the more reason for people to shut up afterwards.