Because our trip was kind of customized I'm can't give a name, but all the mainline travel companies (just picking one randomly, Trafalgar) that specialize in retirees and non-adventure (!) travel do Peru. The question is whether you are willing to pay the price for a multi-day, full-scale product.
Having been there, I would say that the multiple days aren't just to raise income; There's lots to see, and acclimatizing to the altitude is very helpful. (We took medication as well, but had to stop every ten stair steps in Machu Picchu.) Another question is whether you want to buy a product that includes another location, often the Galapagos , or a rainforest boat trip. Of course it costs more, but Machu Picchu is harder to justify all the time and airfare for along. It's a personal budget matter.
Even at a modest luxury level, the early wakeups and multiple plane flights are little grueling. And the less you spend, the more time you have on transport. We deliberately chose a tour with the most expensive, tiny hotel on top of the mountain. But that requires way in advance booking, to avoid the bus ride up after sunrise from Aguas Calientes, where 99% of the non-hiking visitors stay.
Huyana Picchu, which may be the "peak overlooking the site" you mention was our own option during free time. It wasn't paid for as part of the trip, and in fact it is very, very difficult to get one of the limited slots to do each day. In view of our response to the altitude, we were happy not to do it. It's not clear if you were also talking about the multi day, tented hike (relatively level ????) along the trail, which is an alternate to the train to Aguas Calientes.
Edit: I referred indirectly to the fact that the large and chain hotels in that part of Peru tend to have checkout times of 9AM, because of the many early departures, either for planes or the train to Machu Picchu. That means that the (lavish, at bigger places) breakfast buffets open as early as 5 or 5:30AM - I don't mean Continental Breakfast, but the whole thing.
