Nick, back in 1985 when I was 21 for the first time, the situation was much the same but now, as then, there's really not a problem since mainstream insurers can and do offer agreed value policies based on - among other sources of information - the Practical Classics price guide.
PKE was insured on just that basis and I had no trouble with the claim back in 2009 when some fool in a large modern car did the old Dolomite some damage.
That it was actually the 3rd party's insurer who met my claim was perhaps even more encouraging as they were very mainstream and yet had no problem with accepting PC's value of the car along with a valuation form provided by a car club.
So maybe a spot of lateral thinking will find the logical solution which isn't, IMHO, about the fact that "Cherished car" policies won't be available for younger drivers, but that such policies offer no NCB and tend to be limited in other ways when compared to mainstream policies.
Once you become a little older, then there's not even a cost advantage with a cherished car policy, not in every case though obviously some shopping around is required as ever it was with car insurance.
There are exceptions too; Peter James - for example - allowed unlimited mileage and recognised NCB when I insured the Dolomite with them, but I mention that simply because they're not a waste of space rather than as a result of anything that changes the situation for the under 25s.
So in the meantime, insure on a regular policy, far better as you'll accrue NCB, you can agree a value on the car just the same and the premium will still be lower than you'd have to pay for a modern car.
Can't quite see the disadvantage.