You don't need to be riding around on yachts to be rich. If you never need to be concerned about money, you're rich. When I was making $150k a year in SF I didn't need to be concerned about money. At $250k a year, I could invest half my income and still never think about money.
You're not rich if you can forgo thinking about money for only one month.
Being rich is when your job is just for influence and power and not the salary. Being rich is when you can fly from your vacation home in one exotic destination to another exotic destination. Rich is when you have a million dollar painting hanging on your wall that your grandfather acquired in the 1920s for $500. Rich is when you don't even have to think about whether you can afford the private school for all three children with 50k tuition per year each and when you don't even have to think about budgeting for any of it. Rich is when you have a maid at home and a private chef living on your estate. Rich is when your wife can buy the $5000 dress for a one time party and it's not even a wedding or anything special. Rich is when you can afford to hire a doctor to come to your house in this economy. If you live in a 2 BR apartment I don't care how luxurious it is. You're not rich.
If you make less than $500k a year and you don't invest 90% of it you don't even have a chance at being rich in your life time.
We're 10 years away from everyone being a millionaire because inflation is really that high but the difference between barely eking out a 1.1 million dollar net worth based on all your assets and living in a 50 million dollar house may as well be the difference between flying at 30,000 feet and being in actual orbit.
In Dallas, you'd be called upper middle class. In SF, people lecture you that you're "rich".
Post-tax, the difference is only ~$45k. Your rent is going to be an extra ~$20k. Your cost of living is going to be an extra ~$10k.
Okay, so you've got an extra ~$15k, maybe 20% more purchasing power. But this only works if you're single.
If you have kids or a dependent, you're going to lose all of that to rent and expenses (and probably more).
And, until this year, it's not like you could just take your $180k job to somewhere cheaper. If you got a job somewhere cheaper, you'd get paid less to where it wouldn't make much of a difference financially.
Really - the only benefit is how regressive the 401k system is. You can dodge taxes on your high marginal tax rate in SF. So you're much more likely to contribute to your 401k - which will almost certainly work out for you in the long run.
In the short run, you're likely to pay for it significantly with a reduction to your quality of life.
Rich is when you don't need to think about any of this shit at all. People keep trying to put a dollar amount on what being rich is. We're all middle class arguing about how much we make PER YEAR. The truth is you're only rich if you control enough wealth that you can not work for a decade or more.
For example my step father start a trucking business that required him to work from 5 am to 5 pm every day for more than 10 years. Slowly he added more and more drivers. Recently he sold his business for 1.1 million.
Now is he rich? I personally don't think so. They live in a modest townhome in a low cost area. He just has a low burn rate relative to the amount of assets he has. There are way larger houses all around them.
And the truth is most normal people will agree with me because that's what their lives are. What you make per year can't be used as a metric for wealth. It's just earning potential not actual wealth.
These are not terrible apartments, and they're in decent neighborhoods.
These probably would've been closer to $3300 or $3600 pre-covid. And they're not particularly great.
Even with a modest spending budget, if you want to max your 401k - which you will need to do to keep this life style in retirement - you're going to need to make $180k.
Definitely not "hard to live on". But also, you are decidedly far from rich.
$250k - if you are single - you should be able to save a lot and make some investments and have more financial freedom - or more spending, whichever you prefer. Still, you are far from "rich". Even at ~$450k (top 1%), you're going to need several years of savings at that level before you start to feel "rich".
Should people feel sorry for you? No. But are you just riding around on yachts and drinking umbrella drinks all day? No.