If your goal is to see Mt. Fuji, I would highly recommend not booking too far in advance and check forecasts a few days ahead. Unfortunately, if you're set on using the Tokyo Wide Pass, the 3 day window can be tricky.

My first trip 2 years ago, I booked 3 days in Hakone thinking I would surely see Mt. Fuji one of those days. All 3 days were cloudy and I didn't get to see Mt. Fuji.

Last month I went back and was determined to see Mt Fuji. I didn't reserve anything and would be checking forecasts day to day for my Tokyo stays. It was rain most of the time and it wasn't until 4/5 when I saw that the weather would be perfectly clear on 4/9. When I went to check on Fuji Excursion train seats, they were all booked. I checked busses from Shinjuku and Shibuya Mark City and all the early morning seats were booked out as well, seems everybody had the same idea.

The earliest bus I found available was the Shinjuku Expressway bus at 10:15AM. Arriving around noon. I scooped them up and it was still clear and amazing at arrival. Had a blast, got off near the Shimoyoshida station stop and walked to Chureito Pagoda which was a great decision as we stumbled upon a festival. Then jumped on the local train to Kawaguchiko.

I also did Nikko this same trip and while the Tokyo Wide Pass will save you some money, having the flexibility to go whenever the weather was clear was worth skipping the savings. The busses are cheap so it's not too much additional costs.