In Fred W. Riggs' book I now found not only a proof for this statement, but also some further reasons which made the monthon no longer necessary. These further reasons are in fact quoted from the dissertation of Asa Meksavan, who later became governor of Chiang Mai and the last appointed governor of Bangkok.
The counter-revolution of October, 1933, under Prince Boworadet was almost exclusively a result of provincial revolts. It was natural, therefore, for the revolutionists to form an alliance with the [province] governors to eliminate the reyalist lord-lieutenants of the monthon. Since the institution was a new one and one which the governors resented, it seemed easier to eliminate the office than to staff it with new men. [...]Even though that dissertation is already 50 years old - it was published in 1961 - its title "The Role of the Provincial Governor in Thailand" sounds like an really interesting read. Too bad Google Books does not have more than just snippet view of this book.
Arsa offers several factors as possible explanations for this step. He suggests that the spread of modern means of communication no longer made it necessary to have an intervening level between the province and the center in order to secure co-ordination of policy. He also points to the economies which would be made possible in a time of financial stringency (these events took place at the height of a world-wide depression which had grave repercussions in Thailand) by eliminating the igh-prestige and costly monthon offices. Third, it was thought that the monthon had become an administrative and communications "bottleneck" whose removal would step up the efficiency of administrative operations. Finally, the elimination of the monthon was heralded as a democratic measure which would strengthen local autonomy.