The bean counters would still do it without the CEO's direction, since it directly affects the company's ability to pay the employees (including said bean counters) salaries.
Company wide tax mitigation does not happen without C-suite executives being involved. Period. Virtually everything accountants do affects the financial statements and those are reviewed closely by the CEO and his direct reports if they care to keep their jobs. As such it does not happen without oversight with the head of the company leading that oversight.
And they would be under less pressure to do illegal tax dodges, since they would bear direct responsibility for those decisions instead of "just following orders.
Accountants DO bear direct responsibility for their actions and can (and occasionally do) go to jail for "illegal tax dodges". They are the first ones thrown under the bus if something shady is going on. Most tax dodges are 100% legal and there is a cottage industry in finding clever ways to legally reduce tax. The only ones who do it illegally are the ones who are too dumb to know better.
Hang the CEOs, watch the company do better as the people who actually know their jobs do them without outside interference.
If you want to see what a company looks like when you let the accounting and finance people do their jobs "without outside interference" I direct your attention to Enron. What you are proposing is a one way ticket to Fraudtown. A CEO who isn't keeping a close eye on the where the money goes in the company is not doing his/her job and should be fired.