> imagine no market volatility - everything is constant (e.g you've bought bounds)
is where everything breaks down.
Yes, if you keep all your money under your mattress, which is what's actually modeled here (bonds bear interest!) then as long as you don't run out, the unspent amount doesn't matter.
But that would be absolutely bonkers and no one would do it. Instead, you invest in interest-bearing assets. The current inflation-adjusted risk-free rate of return is 1.76%. So if you have a net worth of $2M, you could invest it in bonds and spend $35k a year forever and still pass on the entire principle when you die, essentially guaranteed. If you have a net worth of $500k, on the other hand, you could invest it in bonds and spend $8,800 a year forever.
Of course this would still be crazy - you can get higher yield by taking some risk (and notably, having a higher net worth will allow you to take more risks and get more reward without the risk of running out of money) - but even in the "just buy bonds" scenario, you're much better off with $2M than $500k.