The primary reason why a council will not adopt a private road is cost - why on earth should they? When new estates are planned, the developers do a deal with the council that they will bring the roads up to an adoptable standard (surface, drainage, kerbs). This work is done by the developer, the council inspects then legally agrees to take on future maintenance. This means the the cost of the road is being borne by those buying the new houses (never forget that).
With an unadopted road, the legal owner of it can voluntarily pass it across to the local authority, but they won't take it on unless the road is up to standard in the first place.
So as residents of the road, you have problem: sometimes you are joint owners of the land on which the road runs, when you could band together, fund the road improvement and pass road to the council. If you are not joint owners (but have a legal right of way) you could get the owner to do it. But what's in it for him? - nothing.
The straight answer to both of you is that your solicitor should have advised you the road was unadopted it when you bought it.
The vehicles going down the road is not relevant - do you want your parcels delivered and your bins emptied or not?