That's the same as investment. If a part of society's resources aren't directed towards consumption, they are directed towards enabling future consumption. It's a tautology in economics that savings equals investment.
In any case, one of the major failings of modern macro is to assume you can think your way around the implications of economic actions. You have no way of knowing the consequences of stashing money under a mattress unless you actually do it, and even then there’s no guarantee the effect will be the same across different economies and in different eras. The world is just too complex for that.