The most "fair" way to do it would be to charge according to road wear and tear, which would look something like axle load ^2 * miles driven, but this would be hard to implement and also widely unpopular with huge swathes of the population (truck driver is the most common profession in many states)
The "purpose" of expanding lanes and building alterntae highways is to improve efficiency. For people living in a given area, reduce their time spent commuting. There is large economic cost to having large portions of your population spent 10+ of their waking time commuting to and from work each weekday.
The problem with induced demand is that yes you increase capacity and more people then move clogging up the roads until a similar equilibrum is reached as before. A much better option is both expanding the number of people that can commute by living further out, and reducing the per individual commute time by mass transit. That's the true goal.
That's still an improvement over the previous status quo. Commute times are not the only, or even necessarily the most important factor in a transportation system. Your new equilibrium transports a larger number of people than the previous equilibrium. In isolation, that's purely a good thing.
In a world where road users paid for those improvements directly in proportion to their use of the road we could just keep expanding capacity indefinitely until either all the latent demand were met, or until rising construction costs drove demand down to a level where the roads were no longer congested. Since roads are funded by income taxes though, a crucial half of that feedback loop is missing. We can't just keep expanding because there's nothing to stop road users from demanding more and more capacity even after adding that capacity becomes cost-prohibitive.
So adding roads gets half the benefits (as it doesn't gain any efficiency benefits), and comes with a ton of externalities when compared to mass transit.
Only one I can think of is pollution, but that's not even caused by roads, it's caused by burning gasoline.
Indeed, there's nothing wrong with induced demand on its own. In any other market, more demand induced by lower costs (whether those costs be monetary or in the form of commute times) would almost certainly be a good thing. The only reason it's a potential issue for roads is that road use is an externality.
Building and maintaining efficient roadways comes at a significant cost, but our current system of road construction funded primarily by income taxes means road users don't pay that cost in a manner proportional to their use of those roads. Road construction is "free" from their perspective, so there's no incentive to use alternative means of transportation even if those alternatives would be superior overall once road construction and maintenance costs were factored in.
Because of this it's hard to be sure whether the demand induced by increased supply of roadways is worth the cost in any particular instance. It could be a worthwhile increase in utility, or it could just be a waste of money.
[1]: https://news.ycombinator.com/item?id=28320834