Most, if not all, US administrations have received and/or accepted similar offers, through treaties (1985-12-12, NK accedes to the NPT), directly (1994-06-15, Jimmy Carter brokers a deal to freeze NK nuclear weapons program), with third parties (2000-07-19, agreement with Russia to halt NK missile program / 2002-09-17, agreement with Japan to indefinitely extend missile testing moratorium) and a few others, including those rejected by the US or its' allies.
The thing is, every single one of those treaties, agreements or moratoriums have been torpedoed by three main issues, a base distrust between the two involved blocs of nations, the optics of what each other's activities in the region actually means, and the balance of power in the region.
The first issue is rather banal but very important, on one side you have North Korea, Russia and China; on the other the United States, Japan and South Korea. Two equally balanced blocs each composed of one big power (US, Russia), one small power (Japan, China) and their protectees (South Korea, North Korea). Neither bloc trusts the other, due to an overwhelming number of false moves and broken promises on both sides.
This distrust causes the eastern bloc to be wary of all inspections and requests made by the other side, not trusting that they will be executed in full faith but to be used as an excuse to levy sanctions or other penalties; causing them to cooperate at the minimum level possible in order not to give the other side any excuse to overreach in their conclusions.
On the other side, the western bloc sees the other side as secretive and duplicitous, expecting any and all information given to be incorrect, incomplete or an outright fabrication; causing them to demand maximum cooperation in order to receive as much direct intelligence as possible and not rely on that released by the other side.
Please note I am not making any judgement here; the fact stands that North Korea does hide information and restricts access to that which is minimally necessary for inspections, and the United States does use any inconclusive evidence to levy sanctions in order to push for deeper inspections.
As an example of this distrust, in 1992, North Korea declared some 90 grams of plutonium that, under the current agreement at the time, might be subject to inspection if used for a nuclear weapons program; however, they declared it was the result of processing defective fuel rods for a nuclear power plant; the US pushed the IAEA to nevertheless inspect said plant and imposed sanctions some 20 days later without conclusive evidence.
The second issue is more philosophical, regarding what is "defensive" and what is "offensive". As a basic rule, North Korea regards all US military action in the region as offensive and its own as defensive; the US on the other hand, regards all North Korean military actions as offensive and its own as defensive. In that sense, it would be difficult to achieve any lasting agreement when each side, according to themselves, is simply trying to arm itself against an external actor that is threatening their security.
The third, and perhaps most pertinent issue, is the balance of power. The real global impact of either North Korea scrapping all its nuclear weapons (or even disbanding its military completely) or the United States stopping all military exercises with South Korea (or even withdrawing all its personnel from the region) would be basically null. An undefended North Korea will not cause the US to immediately invade nor would an undefended South Korea cause NK to do the same, nothing would likely happen as there are bigger players at stake.
Neither Russia nor the United States can afford to destabilize the region nor enter into a war, both have large economic and trade dependencies on the nations involved; interestingly, China is the key country in this aspect, as the US would need long-term economic restructuring if it were to lose trade and manufacturing facilities with China and Russia would lose valuable oil export routes to the entire peninsula, possibly causing an economic collapse due to their dependence on oil exports.
So the balance is maintained, Russia pushes North Korea, the US pushes South Korea, and China and Japan try to strike a balance between the two sides.
In essence, North Korea has to continually make the offer and the United States has to continually reject it in order to maintain the status quo.
A few links as requested.
Chronology of U.S.-North Korean Nuclear and Missile Diplomacy -- A pretty good timeline of US NK relations
Energy Relations between
Russia and China:
Playing Chess with the Dragon -- China and Russia energy relationship
An Awkward Dance: China and the United States -- US China trade
U.S. Policy Toward North Korea -- North Korea policy
Lessons from the Capture of the USS Pueblo and the Shootdown
of a US Navy EC-121—1968 and 1969 -- NK incidents
Hans Morgenthau and the Balance of Power in Asia -- Asia balance of power
Creating a Stable Asia: An Agenda for a U.S.-China Balance of Power -- US China balance of power