Starting a company is like building an airplane and trying to fly it straight off a cliff. You might crash, it might be a foolish use of your time, and you might die, but you have a lot of control over whether or not that happens.
Investing in a startup, with the bulk of your savings, is like being a passenger on that airplane.
I imagine most start a company without ever investing money they can't afford to lose. Sure a few $1000 but nothing to make them broke. Instead the money comes from 'loseable savings', family gifts, profits, loans or investors.
Yes but picking between investment opportunities is a bit different than starting a company. If you have enough money to buy a significant chunk in an angel round then you also have enough money to open yourself up to other less risky investment opportunities.
That's lottery style thinking, and will get you the predictable results - almost certainly.
Maybe turning this around will help you see how ineffectual this is:
If you are a naive investor desperate to put all of your small stake into one company and I am an early stage startup, why would I want your money if I can have smart money with a good network instead?
And if I can't have that, if I'm desperate for the investment, well your odds just got much, much worse.
Investing in a startup, with the bulk of your savings, is like being a passenger on that airplane.