The only reason is cash flow.
If a reverse split is not approved, and the company cannot tap into its financing deal, it has two options:
Raise new cash or file for bankruptcy.
There are three paths to raising cash: partner, buyout, or issue new debt.
Let's say someone comes in and offers $75M for the company. If you're management, do you take it? Let's suppose you reject it and file for bankruptcy and somehow the creditors end up getting everything and the shareholders get nothing. The business judgement rule is wide in scope, but this would be a classic case of breach of fiduciary responsibility as you had turned down an offer that would have netted shareholders .12 or so.
Simply put, if the RS fails then management is going to have to enter a partnership or bidding war with zero leverage.
I liken it to this: Either you drive off a cliff by voting against the reverse split, or you drive into a dark forest you're not familiar, and with no headlights by supporting the reverse split Neither is ideal -- but which do you think gives the best chance at living to see another day?