Don't think of it as a large nest egg; think of it as a modest fixed income. You can easily make 2.5MM last for the rest of your life if you're able to live on 100k. That might require downsizing a bit and moving somewhere with a lower COL, but it's certainly doable.
Assuming a 4% return, 2.5MM absolutely does yield 100k per year, forever.
Yes inflation will eat away at the value of that 100k over time, but that's less of a problem if you own your home and have something left over each year to reinvest.
The annualized return on the S&P 500 since its inception is 10 percent. Adjusted for inflation it's 6.5-7 percent. In the last 20 years, it's 5.9 percent. Adjusted for inflation it's 4.37 percent. So withdrawing 4 percent per year would be reasonable and keep up with inflation. It gets slightly more complex when you think about taking money out during down years is much larger impact than during good years, but that's an exercise for the reader.
check firecalc.com for historical likelihood of portfolio success, given a starting nest egg and an annual withdrawal rate. The 4% withdrawal rate mentioned above is very likely to succeed for an indefinite period, and 3% is essentially impossible. This is all assuming 85% US equities and 15% bonds, and that the future looks vaguely like the past 150 years.
Despite all the skepticism above, the 4% claims are true. Not 100% chance of indefinite success, but close enough to be actionable. You can also google the "trinity study" for more info.
If you're buying equities and leaving them alone for decades, sure. But if you're retired and depending on your investments for an income, being 85% in equities is insane. One prolonged bear market could wipe you out.
I'm talking about a fixed income, like bond dividends, annuities, etc. It doesn't adjust for inflation; that's a separate problem. Just saying that if you can get a 4% return on 2.5MM, which is on the high side of realistic, that's a 100k indefinite fixed income.