Velde's observations expose the problem. The following should be considered a speculation...
If the minters explicitly added varying amounts of silver could they have been trying to purposely make the coinage less useful than the hack gold ingots in use at the time? Could the irregular bullion value of early electrum have been a "feature" rather than a "bug"?
It is usually presented that the cementation process of separating gold and silver was an improvement over natural electrum. The story is that when that process became available, under King Croesus, he switched his coinage to the superior bi-metallic system. We aren't sure exactly when the ancients first learned to separate gold and silver, or the precise issue period of early electrum coins. I wonder if the ability to separate gold and silver counter-intuitively caused to the appearance of mixed (electrum) coinage, rather than set the stage for the end of early electrum.
David Graeber points out in his intriguing Debt: The First 5000 Years (2012) that systems of accounting based on debt long preceded coinage. He speculates that coinage was invented as a scheme to provision an army. In Graeber's view, rather than forcing citizens to provide food and materials for an army, a king merely demands a tax in coins he only issues to his army.
Electrum seems perfectly suited to a paranoid king attempting such a scheme. The equipment to separate gold and silver takes a lot of capital to build. Refineries are hard to conceal because of the smoke and smell. It would be easy to have a royal monopoly on parting gold. Mercenaries paid in electrum were less likely to desert if they knew their leader was the only person who could convert their electrum coins into more valuable hack gold.
Such a king could stamp the electrum he issued to his soldiers to ensure the populace equipped the right army. (His army.) I can imagine a lot of warlords running around ancient Lydia, each trying to obtain provisions from local farmers. Attempting a closed currency with identifiable stamped designs seems ideal.
Under such a system the precise weights serve the purpose of discouraging the unscrupulous from hacking or filing off a bit of the coin to keep for themselves. The weight standard can be seen as an anti-clipping technology rather than a promise of fixed bullion value.
Early electrum as a closed military coinage feels correct and compelling, but am I fooling myself? It would be nice to look for confirmation or something that could show the idea to be false. More precise dating could help … if we could show that gold refining was successful before early electrum coins were issued that would lend support. Or if I could find something that suggested early electrum economies were 'closed'.