In the normal course of life, objects which are broken no longer hold value and are readily discarded.
The wonder of the Tablets, however, is that the shattered shards which remained from the first Tablets – broken when Moshe witnessed the sin with the Golden Calf – were deemed important enough to be placed in the Aron within the Kodesh Kodshim.
The Meshech Chochma understands that the error which caused the sin was mistakenly attributing holiness and divinity to objects other than G-d. Rather than viewing Moshe as a channel through which they could receive G-d’s word and thereby worship Him, Moshe himself was deified. When Moshe was absent, they then sought to deify a golden calf in his place. Moshe realized that were he to present the nation with the divinely-formed Tablets at that time they would simply transfer this error onto the stone tablets and revere or worship them too.
For this reason, G-d is said to have congratulated Moshe for shattering the Tablets in front of the people to teach them that objects and places are not inherently holy but only serve, in accordance with G-d’s commands, as a means for man to worship G-d.
The broken tablets were placed in the Ark of the Covenant at the very heart of the Mishkan in order to eternally emphasize this message.