In theory, that implementation of negative income tax (NIT) would cover everyone and seems to have nearly [0] the same effect as a basic income (UBI). However, in practice, the effects will not be equivalent.
With UBI, future checks are already coming, and thus can be relied upon. This gives people the freedom to leave undesirable jobs/relationships without worrying about funding tomorrow's basic needs. With NIT, people would need to apply for an adjustment to their benefits and find a way to self-fund until the application is approved. That hurdle will prevent many from leaving undesirable jobs/relationships and impede numerous others.
As an example, many citizens eligible for food stamps don't {re-}apply. Some don't know they're eligible, some can't navigate the application process, some don't want to go through the application process (many invasive questions, time consuming), and others don't want the stigma of receiving non-universal benefits. [1] [2] With a universal system like UBI, everyone is eligible, the application process can be simple and non-invasive [3], and there is no stigma.[4]
Bonus: UBI (hopefully) allows for elimination of some bureaucracy, instead of folding existing bureaucracy into a new program.
[0] While adjustments can be made to funding and payment structures to make NIT and UBI financially similar, no adjustment in NIT benefit timing addresses the fact that it's non-universal.
