If you're selected for public service, then you're expected to do good for the country, and not just a specific monied interest. And that means not having to worry about money ever again. You win capitalism. Done. Have fun. Live your life.
That could also be done with annuities so that they get a "allowance" each month until dead.
If you have a system in place that can find and punish bribes - why not pay them a reasonable amount of money - and just eliminate bribes without spending $0.1T per year...
Famously, Singapore maintains a very effective, clean civil service by paying market rates, and sometimes for some ministers that is actually millions of dollars a year.
Your worth should be based on your skills (meritocracy) - not by winning the lottery and how much people will pay to influence you (luck).
And with deciding "merit" are the kingmakers, or the "meritmakers".
Congratulations. You now have created a new class of people who can take bribes and subvert leadership under the term "merit".
And, explain how one would calculate "merit"? In my experiences, meritocracies are monocultures that put forth their own biases as "merit".
1: money isn't the only form of bribery.
2: people who want more... will always want more and will never stop taking.
3: there is no good way to tell a person from someone who wants to give to help, and someone who wants to give to get something in return.
A more effective if morally dark methodology is publicly and viscously execute people who take bribes in this system.
As it is, I'm not sure the billion does anything other than ensure that the one policy absolutely every randomly-appointed political figure from the vague woolly liberal to the literal neo-Nazi agrees upon is zero inheritance tax...
Why would they have any incentive to do a good job?
Also, why would they have any desire?
Also, that seems like a lot of money. >95% of people would be happy with the $1M per year salary.