Here’s a hand-wavy estimate. Last year, the personal savings rate in the US was about 8%, so at that rate it would normally take 12.5 years to accumulate 1 year’s income worth of savings, or 6.25 years to save 6 months. If you earned 10% more and saved all of it, and didn’t change anything else about your spending or saving, then your new savings rate would be 16.3%, which would mean it’d take a little over 3 years to save for 6 months. If you previously weren’t saving anything, but you started saving all the extra income from a 10% raise, then your savings rate would be ~9% and it’d take you 5.5 years to save 6 months’ worth of income.

Long.

Because before they can start saving basic needs (home, food, health i.e. mediciens) need to be satisfied and especially the lower percentages might not be able to do so every month with what they earn. Especially health cost might stack up (e.g. a delayed dentist visit because it can't be afforded) and some get more then linearly more expensive when stacked up (small problem with tooth escalated, interests etc.).

So it's not absurd to assume that in the lower percentages of the population getting 110% income will get them at best 10% of a income savings and likely only after some month already passed. With that they would need 60!! month to build up that savings.

Now I can't say where the this stops, is it the lower 5%,10%,20%,30%,40% no idea. But it's gradual.

Also the gap between poor and rich has become quite absurd in the US, so this can make make people much less wealthy then you might think end up in the middle 80%.

Why not just create a simplified welfare state ? Claim benefits for up to six months no questions asked.

Hard to say since ppl are also spending less right now