One of the big issues here is that once employees start selling common stock, the strike price of the options can no longer be set at a large discount to the latest valuation as it can when the only transactions are the preferred stock shares that are sold when the company raises money from VCs.
One of the most attractive things about employee stock options is that the strike price is often set at 30-40% of the valuation of the latest financing round. So a company that just raised (preferred) money at a $500m valuation can give their employees options with strike prices around $200m or less. Therefore, the employee can believe that they have a "locked-in" gain day one.*
If employees sold their common shares at anywhere near fair value at the same time the company was raising the round, they would likely sell at a price between $400m-$500m a very slight discount to the preferred shares. Any future option grants given would have to have a strike price reflective of these recent common-stock transactions, and companies would no longer be able to use the low strike prices of options to attract employees.
Obviously, this is just one trade-off among many and in no way means that companies shouldn't allow more sales of employee common stock over time, but its worth understanding the many reasons companies currently are resistant to doing so as much as individual employees would like.
*Obviously, common shares should be priced at a discount to preferred shares but almost everyone I've talked to in the VC/startup community believes that the 60-70% discount applied is extremely generous as it implies that up 60-70% of the value the VCs investment is in downside protection (ie the debt-like element) rather than upside potential (ie the equity-like element), a pretty nonsensical amount for a high-risk, asset-light VC investment.