IMO the rational for the auto road and cog to subsidize the obs museum is to supply an attraction at the summit for the visitors when weather is not so good. If it is a clear sunny day at the summit, I expect that the museum does not get a lot of visitors, on the other hand if the summit is in the clouds and drizzle whch frequently form in the afternoon I expect the number of museum visitors increases. I dont think the $1 fee is actually to pay a per visitor fee as much as to ensure that it is there if the visitor wishes to visit it. My limited understanding of the history of the fee was it was instituted to help the obs pay for increased summit bills that occurred when the TV station shut down their transmitter. Unlike many of the other summit users, they are a non profit organization so they can not charge fees off to their profit. Not sure how the economics worked previous with the TV station running the powerplant but when the new powerline was built, the cost for the power used had and still has a significant surcharge to pay for the capital expense of running the line up to the summit and ongoing state of NH operating expenses. I do remember there were complaints by the still operating radio stations and communications repeaters that the surcharge was excessive as they were paying the bulk of the expenses for the summit via the surcharge for tourist services they did not need.
Apparently the state's non tourist season staffing increased substantially in recent years as the state now has responsibility to maintain the standby generators at the summit. The obs also has reduced their participation in S&R, in the Goselin era, the obs seemed to be the initial first responder to potential emergencies, this role has reportedly substantially reduced.The obs now has an official statement that they are unable to participate in rescues as they do not have the training or equipment. I have seen reference that the state now have a snowcat for summit access but havent confirmed it. In general under Mike Pelchet's management of the summit after the generator fire, the amount of summit visits by the state increased and all the expenses get added to the surcharge. Many people do not understand that the NH State Park systems is self funded with no state subsidies, they can transfer money between operating units and do get appropriations for capital expenses but the expectation is that each park is at least self supporting so the state expects the summit users will pay the bills.
The reality is that the obs was in very rough financial condition for several years that coincided with the generator fire. There were reportedly a couple of years where the staff was laid off en masse and then rehired due to budget issues. I have no doubt that the fee agreement was a lifeline to the obs by the ownership of the autoroad and the prior ownership of the Cog. It does seem that since the current Cog owner bought out his long term partner and now has 100% control in his family that he has gotten far more vocal and argumentative with the other members of the MWC.
Note that the autoroad was running to the summit a few year before the cog. As the attorney general's ownership summary had stated a few years ago, all the original deeds and surveys of the area are suspect with overlapping claims of ownership and rights to the summit. Even if there is one entity that does have clear title there are numerous overlapping rights and past precedent. I expect no one except for the lawyers litigating the case would be happy with a court settlement.