Perhaps the key point to make here is that Basic Income would not be paid in addition to existing social security payments. It would be paid instead of those payments.
So, at the moment, taxpayers pay to help the poor AND they pay for masses of unnecessary bureaucracy. With Basic Income, they’d still be helping the poor, but they wouldn’t have to pay for all that bureaucratic means-testing too.
I also think it is extremely unlikely that you wouldn’t see any of the benefits of Basic Income. For one thing, you would see the immediate benefit of knowing that Basic Income would be there for you, regardless of how your personal circumstances might change. And if you don’t see that as a benefit, then perhaps you’ve led a more privileged life that you might care to admit.
There are many ways you could benefit from Basic Income, even if it doesn’t make you financially better off. And even if you didn’t personally gain from Basic Income, wouldn’t it make you feel good knowing it was doing so much to help others?