"As long as the requirement for redundancy is satisfied, any type of instrument is allowed."
Is wrong. There are more standards and regulations at play here than is obvious. You can't just "fill the hole" with anything.
Large aircraft must meet the requirements of FAR 25. The standard that requires the standby instruments is FAR 25.1333(b) which reads:
(b) The equipment, systems, and installations must be designed so that one display of the information essential to the safety of flight which is provided by the instruments, including attitude, direction, airspeed, and altitude will remain available to the pilots, without additional crewmember action, after any single failure or combination of failures that is not shown to be extremely improbable.
Extremely Impropable is accepted to represent 1 failure in a billion flight hours. That means the occurance of complete loss of attitude or altitude or airspeed indications must be extremely remote.
The failure rate is calculated by using actual failure data available from the manufacturer of the components. Until recently, no electronic instrument was capable of meeting the failure criteria so "standard steam driven" instruments were used. Some only find their way into cockpits because the basic airplane enjoys triple redundancy for the subject systems.
So, the short answer is that you can use electronic standby instruments to meet the rule only if you can acheive the same required criticality.
One last note, the term "vacuum driven" is causing confusion. Airspeed instruments measure differential pressure between the pitot and static air sources. Altimeters measure static pressure. These instruments are NOT "vacuum driven".
However, SOME gyro horizons are driven pneumatically (vaccum or pressure), and many others are driven electrically. A power source is needed to spin the gyro(s).