And without a proper "coins generating-removable" mechanism, the inflation or deflation will happen very quickly, and currency system won't be stable.
Sure you cannot have truly 'stable' systems (and even current sophisticated system does not work, as indicated by 2008), but back in old days of silver/gold standards it was 'stable enough' without such recycle mechanisms, as amount of currency was limited by amount of silver/gold, which were value by itself.
What's really happening the history of economic history is much more complex than that, and the truly - "good old" gold standard, are not (always) stable at all. Or else we may still using them today. It really has "gold/silver removal" mechanism. (ex. Mughal India is a reservoir for excess gold , because they used silver standard system, treated gold as a commodity).
And as you may think that gold or gold/silver or silver standard system will be stable enough because the "money supply" was fixed due to limit amount of mental exist. But the truth is even that's only half-way true. There are so many combinations of standards already tells us they are not a global standard at all (the true gold standard lived not very long from 18th to early 20th century and only accepted in Europe and their colonies)
On the other hand, the gold/silver mining itself never stops through out human history (till today). And the amount of gold/silver been dug out are not constantly at all, like the discovery and colonization of new world, causing the excessive of gold/silver production. The true reason why a gold/silver standard CAN be used in expansion economics system from 16th to 18th century. And the downfall of gold standard like system, is that although it may be stable as a global exchange system, but again the exactly same reason causing it to be unstable.
Since the growth or recession of productions in economic systems can NOT be reflected by the constant "gold standard". And when a recession do come, The government often seek extreme measure to keep their gold reserve stable, rather than keep the system stable (Every government is selfish like that). And great recession periods like in 1930's and in 1970's, causing it to be abandoned. (Because most reserves in many countries were dried out. After 1970s, gold became a commodity again)
The real "stable" factor in an economic system, often only rely on the "good" government debt and the confidence towards the deferred payment of them by the government. (The government CAN and ABLE to paid back interests and full in the future, whether it's true or not)