It is possible that some employer will allow this. But don't count on it.
One small company I worked for made it clear if you skip participation in the 401K, that increases the companies profits. They budget for the match, and an employee not taking it means they cost them less money to keep.
I have seen companies give extra vacation days if you skip getting the health insurance benefit. But these two things differ in a number of ways. In the US your options for signing up for insurance are limited to open season and life events, so they know you can't easily change your mind. The 401K can be joined at any time, you can adjust your participation every paycheck. Employees that don't need to get insurance from the company have insurance through a spouse or through their military retirement. They aren't generally hurting themselves financially by skipping participation.
The flexibility to join the 401K would severely limit the number of companies that would be willing to give you a bonus for not participating. I know of one place where not participating would cost you money. The company had a match bonus based on company profits. If you didn't participate then that 1-3% of additional match would not end up in the 401K.
Another reason they might not want to reward lack of 401K participation, is that the US government frowns on 401K plans that are biased towards only having highly compensated employees participate. If you assume that younger means lower pay, then the bumped up bonus for not participating may entice employees at the lower end of the pay scale to not participate. When the 401K participation is tilted too heavily towards the higher end of the pay scale, the government then limits how much the highly compensated employees can contribute. Companies want to avoid this.
Putting money into a 401K or IRA when you are young is intimidating. Losing access for decades seems to be a daunting rule. Of course the realization later on that you need to be saving for retirement doesn't allow you to go back in time and put that money into a 401K/IRA.
When people stayed in the same company for decades the idea of putting all your retirement into 401K was both normal and unusual. For the people who were counting on a pension, it was normal to count on one source of retirement funds. For those that expected either a small or no pension the idea of putting money away for decades was daunting.
Now people change companies many times. So they have multiple opportunities to either roll over money from 401K-to-401K or from a 401K into an IRA.