More to the point: living expenses.
If someone starts out with $10k, invests at 5%/y, that's $500/y added.
If that person's rent + food + utility bills are $1000/month, that $500/y is 'peanuts', and other income (like regular job) is needed to make ends meet long-term.
(ignoring inflation for simplicity)
But if starting with $100k, 5% is $5k/y which would cover 5 months/year living expenses. And no worries about losing a job.
Starting with $1m, that's $50k/y interest, or all living expenses covered, no need to have a job, AND $38k/y left over to increase capital or do fun stuff.
That's apart from effect of increases in the cost of living.
So very different effect even if interest % and all else equal. Moving up the ladder from $1k -> $10k -> $100k etc as savings, can take a loooonng time (if possible at all).