It exists, it's called a part time job, and it makes it very hard to do things like "pay rent"
"Part time job" doesn't exist in the sense the person you're replying to (probably) intended. Most of the part time jobs I see are unskilled labour where working full time would already put you at a severe wage disadvantage. These are often designed to exploit students who are piss poor to begin with and can't have a full time job anyway.
Where are all the tech companies that won't turn you down if you send an application in response to their ad for an inevitably full-time position and ask to work half the time for half the salary? Where are all the manufacturing companies or stores or schools or trucking companies that won't turn you down?
The same phenomena has been seen over the last 30 years. When a parent (usually the mother) stayed at home houses were affordable on a single income. After both parents started working prices shot up, now it's essential for both to work, just to pay the extra rent/mortgage. This pushes childbirth later in life, if at all, and means that children are brought up as a factory process rather than parenting.
In the UK this is explicitly encouraged by tax breaks for outsourcing childcare, taxpayer funded childcare, and penalising single working parents through the tax system (60% marginal tax on £50k household income with 1 earner, 33% on £50k household income with two earners, but no way to share tax subsidies)