1 rescue a day would break the state. We are not talking about EMS calls, but in most cases operations involving dozens of people, who many times have to be transported in and housed depending on the area. Those people have other essential tasks they cannot perform while in the field if they are professonals, if volunteer then they are giving up time at work or with families to help others.
If the threat to life is sever enough, than the Coast Guard or Air Force PJ's might contribute a helo with hoist capabilities. Any time you put a helo in the air you are talking a significant increase in risk to rescuers and $25,000 an hour bill to the Federal tax payer if an Airforce Pave Hawk, $9,000 per hour if a Coast Guard Dolphin. If near Anchorage, and distress criteria is not met, if available ot will be a State Trooper bird or LifeMed. LifeMed will send you a $50,000 or so bill and most likely drop you off at an ED where you will get another bill. LifeMed and the Troopers lack hoist capabilities, so if there is not a suitable LZ you are stuck being walked out (sometimes on a litter). If the weather is bad, you had better be able to survive or it will just be a body recovery operation once conditions become safe for rescuers.
Of course, most of the above is similar in some locations in the lower 48, other than remoteness. Alaska is a wild place and nothing south of the Canadian boarder compares in North America, and that includes the Bob Marshall. The furthest you can get from a road in the lower 48 is 21.7 miles in Yellow Stone. I can achieve that without leaving the city limits of Anchorage, even if we consider navigable water as roads.
I know several non-residents get lost following techniques (like following a river) that general work well in the lower 48, but are unlikely to get you closer to civilization in AK.
Unfortunately I don't have data to say if the guide requirement is valid based on SAR costs. I guess the argument is that Brown Bear is a dangerous animal, and sheep and goats put people in harsher terrain. Which is why for US citizens the guide requirement does not apply to all big game. Non-resident aliens need a guide to hunt any big game, so it could be worse.
If SAR was the driving force behind the guide requirement I would expect a permitting system like that for climbing Denali where prior experience was taken into acout for resident and non-resident alike. However, in the absence of data, I could be wrong about that assumption.