The design purpose of the Bill of Rights was to protect the people from government impositions. Do you think that people who wrote it, with that purpose in their minds, were worried that the State would ban their own State Police from carrying firearms, and that's what they should prevent? How would that even look like - the Government will issue an edict that no Government employee is allowed to carry firearms, even in law enforcement, but the Courts would come in and say - no-no-no, your police has the right to bear arms! So you must have the armed police, whether you want it or not!

This sounds completely contrary to what in practice every government on Earth does. Of course the State can arm their agents, if they want to - you don't need to specially mention it as a fundamental right, as you don't need to specially mention they are allowed to breathe or eat - that's how it always happens. What doesn't always happen and needs special protection - is the right of the citizens which are not government agents, and thus the government - which always has a lot of armed people in their employ - can easily walk all over them. To mitigate it somewhat was the exact purpose of the Bill of Rights.