I think the messaging was intended to create a psychological effect rather than a budgetary one. By voluntarily giving up a benefit to stay with the federal government post-Musk takeover, employees may feel more committed to the new regime. IIRC Zappos used to offer people a payout to leave directly after hiring them, it was a similar signal of commitment.
1. Under RIFs, close to half of the civil service will get a better severance than this offer. So any thinking person would wait for a RIF.
2. Under VERA, people will lose this "severance" but get access to their pensions years earlier. Since VERA only applies if you have 20+ years (25 if under 50) that's 20+% of their current high-3 for the rest of their lives, sets a nice baseline income. A WG employee who started at a depot at age 18 could collect their pension starting at age 43 and get $20-30k/year for the rest of their life and still be young enough to get another job and keep earning until 60 and retire a second time.
3. A substantial number of federal employees are already working on-site (not necessarily in offices) in areas where there are not a ton of other jobs. Ask a civil servant at China Lake to resign, they have to move too, there are few jobs in the area besides that base.
4. Many federal employees are federal employees because they care about the mission. They'd rather keep doing what's been asked of them to keep things like critical infrastructure operating than go home and let things fall apart because no one is doing the work.
The problem is that the new regime appears to be more interested in amputation than footwear for most of these depts/agencies. Those less committed to their mission of walking and running will leave. Those left behind will be the more intransigent veteran operators, "somebody has to keep everyone's feet attached".