Paraphrasing from another answer:
You can do that, but shareholders can also do the following in response:
1) Demand a change in leadership, a sale, or any number of significant changes.
2) Bail out en masse and sell, lowering the price even further. Few investors want to jump aboard what appears to be a sinking ship.
Eventually you'll hit the minimum market cap requirement as well, at which point a reverse stock split won't save you from being delisted.
Reverse stock splits simply to avoid being delisted is telling investors "we have no idea how to change direction so we're just gonna kick the can down the road for a bit". They can work sometimes, mostly for:
1) Large, established companies (e.g. AIG). Investors are more willing to believe that this is just a bad stretch for an otherwise valuable company.
2) Inherently risky and volatile industries, like Biotech. Investors are willing to roll the dice a bit more with Biotech because it is entirely possible for a "worthless" company to become very valuable very quickly (e.g. by discovering a new drug, being approved for trials, etc.).
Blue Apron isn't a large company, and it's very unlikely they figure out some magic formula that makes their company significantly more valuable overnight.
EDIT: For a recent example of a company reverse splitting to avoid delisting, check out Helios and Matheson (MoviePass). Even after the reverse split, they're trading for pennies a share. They're almost certainly going to be delisted in the near future.