That's elective. It's fine and not uncommon to just give employees stock (actual shares, not options) in a company as compensation. Famously Wizards of the Coast gave shares to employees and vendors to create alignment.
Someone is going to point out that giving actual shares is a taxable event. And that is sometimes the rational for options. But there are work arounds: you can put shares in a 401k for example. 401ks were originally created to be employee incentives, but morphed into being used for retirement, but you can still do it either way.
There are a lot of ways to do this. However you should NEVER have any significant value in the stock of the company you work for. It has happened - and will happen again - that the company you work for goes bankrupt unexpectedly and now not only are you out of a job but your savings has vanished as well! Even if the company is doing well you need to diversify your savings out of that one basket.
There is one exception: if you are high enough in the company that you actually know the non-public information as it happens (not either because you need to know or months later in the all-employee meeting). Then the shareholders demand you hold a lot of value in the company so that if you do something bad for the company it hurts. Most of us will never be that high.
Financial advisors will advise you against the risk of having all your wealth in the company you work for for just the reason you describe. If you have a net worth of $10m and it is all in the company you work for you could in one moment loose your job and be broke. So you should diversify.
However, employees often have virtually no net worth (why else are they worried about paying taxes on share, except they can't take the risk of loss? I can say from experience that when I worked for a startup but had previous personal financial success I just absorbed the tax bill for exercising options knowing that the shares I paid taxes on could ultimately be worthless.).
So if all their net worth is in a company its not ideal but it is a risk you can take when you are young. I see the argument of avoiding taxes and not taking ownership until the shares are liquid-- good arguments, it is true-- as being used as ways to justify giving employees shares or options that are likely to be less valuable then the ones held by founders and investors.
If you have almost no net worth than put it in a bank savings account. If you have more than almost nothing put it in 401k or IRA plans - a house is sometimes a good option too (but only if you will live there for a decade, and of course ___location ___location ___location). Only when you have the above in great shape should you thinking about anything else more risky.
Someone is going to point out that giving actual shares is a taxable event. And that is sometimes the rational for options. But there are work arounds: you can put shares in a 401k for example. 401ks were originally created to be employee incentives, but morphed into being used for retirement, but you can still do it either way.