I'm not saying this is going to be the case, but be aware that the day or two a week in office may turn into three or more days a week, depending on how low on the totem pole you are.

I actually moved to DC from NYC for work after trying to commute for a week. It absolutely was not worth the extra stress to tack on an extra 7+ hours of travel time per week, considering all the potential pitfalls of delays or oversleeping. I was thinking the same as you, that I could make it worthwhile through frequent traveler/hotel bonuses. Ultimately, the cost of staying + commuting vs moving was about even, but I had way less free time.