There's been a really strong and justified precedent set for using regulation for this; drunk driving. In fact, regulation for impaired elderly drivers may be even more justified than it is for drunk driving. (I'm not defending drunk drivers, here, just to get that out of the way. Driving while drunk is an incredibly stupid decision.)
Drunk drivers are only impaired some of the time, whereas many elderly drivers are impaired all the time. Because of this, it's possible to test, in advance, whether or not an elderly driver is safe behind the wheel. You can't give a drunk a sobriety test every 12 months to certify them safe to drive; you could do that for elderly drivers.
Enforcing testing for elderly drivers also has the advantage of being a largely preventative measure, rather than a punitive one. The demographic it targets is also more likely to obey or respect that law, generally has more options for free or cheap transit, and is likely to be more deterred by the prospect of a sentence.
The downside, of course, is that being old is not a preventable condition; ompaired elderly drivers don't go out to the Frothing Otter on weeknights for bottled arthritis. Drunk driving can be easily demonized because the drunk driver made a choice to be impaired. The elderly can't be demonized for being too old or crippled, so it would be hard to push anything through. They're also extremely sympathetic defendants.
Elderly driving certification is certainly bad PR. But it's as justified as the original drunk driving laws. (Original meaning before they evolved into the nightmare they are today.)