There are several unanswered questions, such as which kind of businesses are failing more, or starting less; and how do US trends compare to other countries? And, are they counting everybody? For example, volume Ebay sellers could be considered "entrepreneurs" but may not formally register as a business.

Online and "big-box" stores have almost certainly reduced mom-and-pop retail, at least physical stores. Does this account for the entire drop, or just a part of it?

As far as blaming "regulations", I'd like to see some specific examples. Many times they are state or local regulations. Don't focus only on Federal regs.