IB -> PE/GE -> MBA -> Entrepreneurship?

Curious to see if anyone has followed this path as it is something that I am considering, are there any pros to following this path vs, starting entrepreneurship flat out?

Pros I've considered:

1. Strong background in finance = more credibility when raising funding

2. Network (BB -> MF -> HBS/GSB)

3. "stamp of approval" - the pedigree gives more credibility and approval

4. MBA can meet some smart people and form a well positioned/balanced team

Cons:

1. Loss of time

2. IB and PE are somewhat irrelevant to entrepreneurship but I do feel like you can apply most of the knowledge

3, Cost of MBA (Not really problem personally)