It isn't just coin dealers and the ACCG that think lack of property rights causes looting. a letter from the Numismatic Society to the Lords Commissioners from 1871 makes the same point.
An article by M. Adrien Blanchet, translated into English by Herbert Grueber, “Treasure-Trove, its Ancient and Modern Laws” (Numismatic Chronicle, 1902, p. 148) provides many alternatives to the current scheme:
The old Roman right leaves us to understand that a citizens who unearthed a treasure, even on ground which belonged to him, should hand it over to the fiscus.  ....
Nerva, with his accustomed liberal spirit, surrendered his rights to a treasure found by Atticus, the father of the Sophist Herod, on his own lands. 
Under Constantine the Great, the public treasury insisted on its rights; and a law of A.D. 315 granted to the finder one-half of the treasure, when duly announced to the fiscus. The same text provides that no enquiry shall follow, if such declaration be made in proper form. 
In a mandate of Philip IV, dated 27th August, 1306, it is ordered that treasures without any distinction found on lands or in dwellings belonging to Jews shall be surrendered to the King. 
Without going into detail, we may mention that in Denmark, according to the law of Valdemar I,  it is enacted that if anyone should find gold or silver in a field or on a hill or under his plough, it belongs to the King; and if he denies that he has found it, let him defend himself on oath before his kinsmen.
In Italy the State possesses also the right of pre-emption, the application of which has greatly fostered the concealment of treasure-trove, as the proprietors are ware of the small indemnity offered by the State. In mediaeval times the law appears to have been different, at least at Padua; for in 1274 we learn "that a treasure of pure gold of supposed value of more than 30,000 livres was found in the garden of the Hospice of the Domus Dei at Padua, which was unfairly divided byeween the finders, the Bishop, and the State and its officials; a fourth part being, however, reserved for the Hospital, but subject to the conditions that it should be devoted towards its repair."
In discussing the question of the origin of the English Common Law of Treasure-Trove, Professor E. C. Clark  is of opinion that there is little or no direct trace of a Roman original. The claim for the Crown would seem rather to be derived from some such feudal doctrine as that of ultimate ownership of land being vested in the Lord Paramount. Such a docutrine is not of Italian growth, but much more Teutonic in character. In Anglo-Saxon times the right of the Crown or Lord Paramount appears never to have been questioned ....
In 1886 the discovery of a hoard of gold coins of Henry VI-VIII at Park Street, St. Albans, was the means of bringing about a futher improvement in the conditions of recompense to finders of treasure-trove, and in this improvement was mainly due to the strenuous efforts made by our President, Sir John Evans. On that occasion our President pointed out to the Treasury that the system ... of giving the finders merely the intrinsic value of coins retained, whilst the Treasury received from the Trustees of the British Musuem and other public institutions the archaeological or numismatic value of the coins, was a very unjurious and unfare one....
Already in the country districts the cultivator of the soil is inclined to resent the interference of the State with his personal affairs; and I do not fear contradiction when I state that numerous finds of coins, jewellery, or other small objects of antiquity have been dispersed and even melted down before being studied, and that because the finder imagines that the State has an absolute right over all finds. This feeling is probably the result of the influence of the various customs ... which have been enumerated above.
For numismatics in particular it is of the highest importance that the treasures should be preserved in the entirety and also that their provenance should be known.