If I had over 10k in savings I would try to invest at least some of it in something that would give a marginal return in a few years. It would be better than just letting it sit in a savings account.
A 40 is not liquid - if something happens and you need money tomorrow yo don't have immediate access to those funds. There may also be heavy fees if you pull funds out before you are 60.
If I had 15k in savings to buy a house in two years I could put 10k into a CD and still make something like $300. The 5k could be for emergencies and the 10k is still more liquid than a 401k.
This is not an option for a lot of people, particularly those with families.
That said, your follow-up makes sense, and I've typically done something similar.
Back in 2008 any job (even fast food) was hard to come by in my area.
Regardless less than $1000.00 on hand for emergency for the majority is disturbing.