Even today, lots of people have the issue where if they _have_ money, they are compelled to spend it on frivolous things like entertainment and alcohol. Layaway was an easy and convenient tool that people could use to make sure they were putting at least some of their money toward things they really wanted.
Incidentally, where do you live that the interest on a mere savings account is worthwhile on a timescale of years rather than decades or centuries? Or am I taking "savings account" too literally when you mean things like certificates of deposit or money-market accounts?
You are making dhosek’s argument for them.
Because if it's immediately available in a savings account, the vast majority of people are much more likely to spend it on something else. The appeal of layaway is the willpower enforcement - worth the price of whatever pocket change you're likely to get in savings-account interest.