Nobody should be "saving" anything beyond ~twice the month income amount. People should invest the rest instead. Putting money on hold means getting the whole idea of money wrong. Money is not a value itself, it's a productivity measurement unit.
This is an over simplistic view that applies broad strokes. I hold the view that cash flow is king. Without having significantly more than 'twice the month income' right now I would be unable to pay my rent and bills and be forced to pick up lower income work at the opportunity cost of finding a new job that's in line with my career.
I think how much someone should save vs. invest depends so much on the person's circumstances. How big does your emergency fund need to be to give you general peace of mind in life? What are your goals? How long term vs. short term are these goals? What's your career plan and/or trajectory? All these things matter a lot.