This causes deflationary pressures upon the market that cripple the entire market and ultimately empower the rich.
Removing the influx of cookies means that the value of cookies will go up over time, so no one will spend cookies beyond what they need to. Thus, people will choose not to spend their cookies on discretionary goods, things like toys and books and electronics and restaurants that are not necessary but are still important sections of the economy.
Additionally, since you can only save non-essential cookies, you create a system that disproportionately affects people for whom essential goods are a larger percentage of their total income.