Its worse: you search for a government service, like issuing a passport or a driving lisence, that by law and by logic only the government can provide , and the top result is often a scam.
To be fair to Google, they've only known about this issue for at least 10 years and I'm sure they are working hard on fixing it. It's not as easy as you think since the only legitimate domains in such a scenario would be .gov and there isn't any available technology to whitelist this tld - as far as I know?
When my household moved last year two of the adults fell for this scam with change of address. For the record USPS will change your address for free in person or for $1 online (using a credit card cuts down on fraud and they have to charge something to actually use the CC). Well two people fell for bullshit Google ads and paid $85 each. One got her money back. The other did not. I am sure Google will fix it any day now.