Die Stadt war voller hungriger Soldaten.

The use of the genitive case in this sentence is surely inappropiate. Would not “Die Stadt war voll von hungrigen Soldaten.” be better,?

Both work. “voll von” is just another example of the exctinction tendency of the genitive by replacing it with prepositions and the dative case. But “voller Soldaten” is still perfectly valid and in use.

Thank you for your comment which is consistent with my perception from other sources that the genitive case is steadily falling into disuse especially in spoken German.